Question 1

Find the Probability of One Event or a Second Event Occurring
-A card is drawn from a deck of 52 cards. What is the probability that it is a 6 or a diamond?

Accepted Answer

The answer of Find the Probability of One Event or...

Question 2

Find the Probability of One Event or a Second Event Occurring
-A card is drawn from a deck of 52 cards. What is the probability that it is a picture card (Jack, Queen, King) or a heart?

Accepted Answer

The answer of Find the Probability of One Event or...

Question 3

Find the Probability that an Event Will Not Occur
-A bag contains 20 marbles, of which 3 are blue and 7 are green. One marble is drawn from the bag. What is the probability that the marble drawn is not blue?

Accepted Answer

The probability that the marble drawn is not blue is 1 minus the probability of drawing a blue marble. There are 3 blue marbles out of 20, so the probability of not drawing a blue marble is $1 - \frac{3}{20} = \frac{17}{20}$.

Question 4

Find the Probability of One Event or a Second Event Occurring
-One digit from the number $5,929,119$ is written on each of seven cards. What is the probability of drawing a card that shows 5,9 , or 2 ?

Accepted Answer

The number 5,929,119 contains the digits 5, 9, and 2, which are the digits of interest. There are two 9s, three 1s, one 5, and one 2. Therefore, there are 2 (for 9) + 1 (for 5) + 1 (for 2) = 4 cards out of 7 that show a 5, 9, or 2. However, since the question asks for the probability of drawing a card that shows any of these digits and there are two 9s, the correct count of favorable outcomes is 2 (for 9) + 1 (for 5) + 1 (for 2) = 4, but the total number of cards is 7, and we are interested in the probability of drawing either of these digits, not the count. Given the misunderstanding in the explanation, the correct approach is to identify the total number of desired outcomes (4) and divide by the total number of outcomes (7), which indeed results in $\frac{4}{7}$, aligning with choice C, not A, based on the correct interpretation of the question.

Question 5

Find the Probability of One Event or a Second Event Occurring
-Give the probability that the roll of a die will show 4 or 6 .

Accepted Answer

The probability of rolling a 4 or a 6 on a die is $\frac{2}{6}$ because there are 2 favorable outcomes out of 6 possible outcomes, which simplifies to $\frac{1}{3}$.

Question 6

Find the Probability of One Event and a Second Event Occurring
-A card is drawn from a well-shuffled deck of 52 cards. What is the probability of getting a red 4 ?

Accepted Answer

There are 2 red 4s in a deck of 52 cards (one from hearts and one from diamonds), so the probability is $\frac{2}{52}$ which simplifies to $\frac{1}{26}$.

Question 7

Find the Probability of One Event or a Second Event Occurring
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What is the probability that the arrow will land on 5 or 2 ?

Accepted Answer

The answer of Find the Probability of One Event or...

Question 8

Find the Probability of One Event and a Second Event Occurring
-Two 6-sided dice are rolled. What is the probability that the sum is odd and the number on one of the dice is a 3 ?

Accepted Answer

The answer of Find the Probability of One Event and...

Question 9

Find the Probability of One Event or a Second Event Occurring
-Give the probability that the roll of a die will show a number less than 4 .

Accepted Answer

A standard die has six faces numbered 1 through 6. The event of rolling a number less than 4 includes the outcomes 1, 2, and 3, which are 3 out of the 6 possible outcomes. Therefore, the probability is $\frac{3}{6} = \frac{1}{2}$.

Question 10

Find the Probability of One Event or a Second Event Occurring
-One digit from the number $8,161,441$ is written on each of seven cards. What is the probability of drawing a card that shows 8 or 4 ?

Accepted Answer

The number 8,161,441 has three occurrences of the digit 4 and one occurrence of the digit 8, making a total of 4 favorable outcomes. Since there are 7 digits in total, the probability of drawing a card that shows 8 or 4 is $\frac{4}{7}$.

Question 11

Find the Probability of One Event and a Second Event Occurring
-A 6 -sided die is rolled. What is the probability of rolling a number that is even and a 5 ?

Accepted Answer

The events are mutually exclusive since a number cannot be both even and 5 at the same time.

Question 12

Find the Probability of One Event or a Second Event Occurring
-A spinner has regions numbered 1 through 15 . What is the probability that the spinner will stop on an even number or a multiple of 3 ?

Accepted Answer

The even numbers between 1 and 15 are 2, 4, 6, 8, 10, 12, and 14, giving us 7 even numbers. The multiples of 3 between 1 and 15 are 3, 6, 9, 12, and 15, giving us 5 multiples of 3. However, 6 and 12 are counted in both categories, so we don't double-count them, leaving us with 7 + 5 - 2 = 10 unique numbers that are either even or multiples of 3 out of 15. Therefore, the probability is $\frac{10}{15} = \frac{2}{3}$.

Question 13

Find the Probability of One Event and a Second Event Occurring
-If two 12 -sided dice are rolled what is the probability that both numbers will be even?

Accepted Answer

The probability of rolling an even number on a 12-sided die is $\frac{6}{12} = \frac{1}{2}$, since there are 6 even numbers (2, 4, 6, 8, 10, 12) out of 12 possible outcomes. The probability of both dice rolling even numbers is $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$.

Question 14

Find the Probability of One Event or a Second Event Occurring
-A lottery game has balls numbered 1 through 15 . What is the probability of selecting an even numbered ball or a 13?

Accepted Answer

The even-numbered balls are 2, 4, 6, 8, 10, 12, 14, making 7 even-numbered balls. Including the number 13, there are 8 favorable outcomes out of 15 possible outcomes, so the probability is $\frac{8}{15}$.

Question 15

Find the Probability of One Event or a Second Event Occurring
-What is the probability that the arrow will land on an odd number?

Accepted Answer

The answer of Find the Probability of One Event or...

Question 16

Find the Probability of One Event or a Second Event Occurring
-A card is drawn from a deck of 52 cards. What is the probability that it is a heart or that it is greater than 3 and less than 10 ?

Accepted Answer

The probability of drawing a heart is $\frac{13}{52}$ since there are 13 hearts in a deck. The cards greater than 3 and less than 10 are 4, 5, 6, 7, 8, 9, which are 6 cards per suit, totaling 24 cards across all suits. However, 6 of these are hearts, which we've already counted. So, we add the unique cards (18 non-heart cards in the range) to the hearts, giving us 31 unique cards that satisfy either condition. Thus, the probability is $\frac{31}{52}$.

Question 17

Find the Probability of One Event or a Second Event Occurring
-A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 8 ?

Accepted Answer

The probability of drawing an ace is $\frac{4}{52}$ since there are 4 aces in a deck of 52 cards. Similarly, the probability of drawing an 8 is $\frac{4}{52}$ since there are also 4 eights. The events are mutually exclusive, so the probability of drawing an ace or an 8 is the sum of the two probabilities: $\frac{4}{52} + \frac{4}{52} = \frac{8}{52} = \frac{2}{13}$.

Question 18

Find the Probability of One Event or a Second Event Occurring
-Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 5, 6, or 1 ?

Accepted Answer

There are 3 favorable outcomes (drawing a 5, 6, or 1) out of 10 possible outcomes, so the probability is $\frac{3}{10}$.

Question 19

Find the Probability of One Event or a Second Event Occurring
-Given the sequence $7,8,9,10 \ldots 44$, what is the probability that a number in the sequence is even or that it is greater than 10 and less then 25 ?

Accepted Answer

The sequence has 38 numbers. There are 19 even numbers and 14 numbers greater than 10 and less than 25. The overlap is 7 numbers (12, 14, 16, 18, 20, 22, 24). Using the formula for the probability of either event: P(A or B) = P(A) + P(B) - P(A and B), we get (19 + 14 - 7)/38 = 26/38 = 13/19.

Question 20

Find the Probability of One Event or a Second Event Occurring
-A card is drawn from a deck of 52 cards. What is the probability that it is a numbered card (2-10) or a club?

Accepted Answer

There are 40 numbered cards (2-10) and 13 clubs in a deck of 52 cards. So, the probability of drawing a numbered card or a club is:P(numbered card or club) = P(numbered card) + P(club) - P(numbered card and club)= 40/52 + 13/52 - 0= 53/52

Quiz 11: Sequences, Induction, and Probability

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a deck of 52 cards. What is the probability that it is a 6 or a diamond?

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a deck of 52 cards. What is the probability that it is a picture card (Jack, Queen, King) or a heart?

Find the Probability that an Event Will Not Occur -A bag contains 20 marbles, of which 3 are blue and 7 are green. One marble is drawn from the bag. What is the probability that the marble drawn is not blue?

Find the Probability of One Event or a Second Event Occurring -One digit from the number $5,929,119$ is written on each of seven cards. What is the probability of drawing a card that shows 5,9 , or 2 ?

Find the Probability of One Event or a Second Event Occurring -Give the probability that the roll of a die will show 4 or 6 .

Find the Probability of One Event and a Second Event Occurring -A card is drawn from a well-shuffled deck of 52 cards. What is the probability of getting a red 4 ?

Find the Probability of One Event and a Second Event Occurring -Two 6-sided dice are rolled. What is the probability that the sum is odd and the number on one of the dice is a 3 ?

Find the Probability of One Event or a Second Event Occurring -Give the probability that the roll of a die will show a number less than 4 .

Find the Probability of One Event or a Second Event Occurring -One digit from the number $8,161,441$ is written on each of seven cards. What is the probability of drawing a card that shows 8 or 4 ?

Find the Probability of One Event and a Second Event Occurring -A 6 -sided die is rolled. What is the probability of rolling a number that is even and a 5 ?

Find the Probability of One Event or a Second Event Occurring -A spinner has regions numbered 1 through 15 . What is the probability that the spinner will stop on an even number or a multiple of 3 ?

Find the Probability of One Event and a Second Event Occurring -If two 12 -sided dice are rolled what is the probability that both numbers will be even?

Find the Probability of One Event or a Second Event Occurring -A lottery game has balls numbered 1 through 15 . What is the probability of selecting an even numbered ball or a 13?

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a deck of 52 cards. What is the probability that it is a heart or that it is greater than 3 and less than 10 ?

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 8 ?

Find the Probability of One Event or a Second Event Occurring -Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 5, 6, or 1 ?

Find the Probability of One Event or a Second Event Occurring -Given the sequence $7,8,9,10 \ldots 44$ , what is the probability that a number in the sequence is even or that it is greater than 10 and less then 25 ?

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a deck of 52 cards. What is the probability that it is a numbered card (2-10) or a club?

Quiz 11: Sequences, Induction, and Probability

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a deck of 52 cards. What is the probability that it is a 6 or a diamond?

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a deck of 52 cards. What is the probability that it is a picture card (Jack, Queen, King) or a heart?

Find the Probability that an Event Will Not Occur -A bag contains 20 marbles, of which 3 are blue and 7 are green. One marble is drawn from the bag. What is the probability that the marble drawn is not blue?

Find the Probability of One Event or a Second Event Occurring -One digit from the number 5,929,1195,929,1195,929,119 is written on each of seven cards. What is the probability of drawing a card that shows 5,9 , or 2 ?

Find the Probability of One Event or a Second Event Occurring -Give the probability that the roll of a die will show 4 or 6 .

Find the Probability of One Event and a Second Event Occurring -A card is drawn from a well-shuffled deck of 52 cards. What is the probability of getting a red 4 ?

Find the Probability of One Event or a Second Event Occurring - What is the probability that the arrow will land on 5 or 2 ?

Find the Probability of One Event and a Second Event Occurring -Two 6-sided dice are rolled. What is the probability that the sum is odd and the number on one of the dice is a 3 ?

Find the Probability of One Event or a Second Event Occurring -Give the probability that the roll of a die will show a number less than 4 .

Find the Probability of One Event or a Second Event Occurring -One digit from the number 8,161,4418,161,4418,161,441 is written on each of seven cards. What is the probability of drawing a card that shows 8 or 4 ?

Find the Probability of One Event and a Second Event Occurring -A 6 -sided die is rolled. What is the probability of rolling a number that is even and a 5 ?

Find the Probability of One Event or a Second Event Occurring -A spinner has regions numbered 1 through 15 . What is the probability that the spinner will stop on an even number or a multiple of 3 ?

Find the Probability of One Event and a Second Event Occurring -If two 12 -sided dice are rolled what is the probability that both numbers will be even?

Find the Probability of One Event or a Second Event Occurring -A lottery game has balls numbered 1 through 15 . What is the probability of selecting an even numbered ball or a 13?

Find the Probability of One Event or a Second Event Occurring -What is the probability that the arrow will land on an odd number?

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a deck of 52 cards. What is the probability that it is a heart or that it is greater than 3 and less than 10 ?

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 8 ?

Find the Probability of One Event or a Second Event Occurring -Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 5, 6, or 1 ?

Find the Probability of One Event or a Second Event Occurring -Given the sequence 7,8,9,10…447,8,9,10 \ldots 447,8,9,10…44 , what is the probability that a number in the sequence is even or that it is greater than 10 and less then 25 ?

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a deck of 52 cards. What is the probability that it is a numbered card (2-10) or a club?

Find the Probability of One Event or a Second Event Occurring -One digit from the number $5,929,119$ is written on each of seven cards. What is the probability of drawing a card that shows 5,9 , or 2 ?

Find the Probability of One Event or a Second Event Occurring -One digit from the number $8,161,441$ is written on each of seven cards. What is the probability of drawing a card that shows 8 or 4 ?

Find the Probability of One Event or a Second Event Occurring -Given the sequence $7,8,9,10 \ldots 44$ , what is the probability that a number in the sequence is even or that it is greater than 10 and less then 25 ?