Question 1

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 2

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 6?

Accepted Answer

The probability of drawing an ace is $\frac{4}{52}$ since there are 4 aces in a deck, and the probability of drawing a 6 is also $\frac{4}{52}$ since there are 4 sixes. Since these events are mutually exclusive (you can't draw an ace and a 6 at the same time with one card), you add the probabilities: $\frac{4}{52} + \frac{4}{52} = \frac{8}{52}$, which simplifies to $\frac{2}{13}$.

Question 3

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 in hearts and one in diamonds), so the probability is $\frac{2}{52} = \frac{1}{26}$.

Question 4

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 heart?

Accepted Answer

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

Question 5

Find the Probability of One Event or a Second Event Occurring
-Give the probability that the roll of a die will show 6 or 1.

Accepted Answer

The probability of rolling a 6 is $\frac{1}{6}$, and the probability of rolling a 1 is also $\frac{1}{6}$. Since these are two mutually exclusive events, their probabilities can be added together, resulting in $\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$.

Question 6

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 diamond or that it is greater than 2 and less than 9?

Accepted Answer

The probability of drawing a diamond is $\frac{13}{52}$ since there are 13 diamonds in a deck of 52 cards. The probability of drawing a card greater than 2 and less than 9 (3, 4, 5, 6, 7, 8) is $\frac{6}{52} \times 4$ (since there are 4 suits) which equals $\frac{24}{52}$. However, since the diamonds that are greater than 2 and less than 9 have been counted twice, we subtract the overlap (6 diamonds) once: $\frac{13}{52} + \frac{24}{52} - \frac{6}{52} = \frac{31}{52}$.

Question 7

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 1 or a spade?

Accepted Answer

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

Question 8

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

There are 5 odd numbers on the dartboard (1, 3, 5, 7, 9) out of a total of 10 numbers. Therefore, the probability of landing on an odd number is $\frac { 5 } { 10 }$ which reduces to $\frac{1}{2}$.

Question 9

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 1 ?

Accepted Answer

Since the arrow can only land on one number at a time, the probability of it landing on 5 OR 1 is calculated by adding the individual probabilities of it landing on 5 and 1. 
The probability of the arrow landing on 5 is 1/5 and the probability of it landing on 1 is 1/5. 
So, the total probability of it landing on 5 OR 1 is:
1/5 + 1/5 = 2/5 
Therefore, the probability of the arrow landing on 5 or 1 is 2/5, which is option A.

Question 10

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 that the card will have a value of 3 and be a face card?

Accepted Answer

A card cannot simultaneously have a value of 3 and be a face card, so the probability of both events occurring is 0.

Question 11

Find the Probability of One Event or a Second Event Occurring
-Given the sequence 3, 4, 5, 6 ... 42, what is the probability that a number in the sequence is even or that it is greater than 12 and less then 27?

Accepted Answer

The sequence from 3 to 42 has 40 numbers. The even numbers in this sequence are every other number, so there are 20 even numbers. The numbers greater than 12 and less than 27 are 13 through 26, which are 14 numbers. However, 7 of these are even (14, 16, 18, 20, 22, 24, 26), which we've already counted. So, we add the unique odd numbers in this range (7) to the total even numbers (20) to avoid double-counting, giving us 27 unique numbers that meet either condition. Thus, the probability is $\frac{27}{40}$.

Question 12

Find the Probability of One Event or a Second Event Occurring
-One digit from the number 4,696,336 is written on each of seven cards. What is the probability of drawing a card that shows 4 or 3?

Accepted Answer

There are 3 cards with 4 or 3 on them (4, 3, 6). There are 7 cards total. So the probability is 3/7.

Question 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 picture card (Jack, Queen, King)or a heart?

Accepted Answer

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

Question 14

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 4, 7, or 3?

Accepted Answer

There are three desired outcomes (drawing 4, 7, or 3) out of a total of ten possible outcomes (drawing any ticket). Therefore, the probability is $\frac{3}{10}$.

Question 15

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 7?

Accepted Answer

The even-numbered balls are 2, 4, 6, 8, 10, 12, 14, making 7 even-numbered balls. The number 7 is also an option but is not even, so it adds one more unique outcome, making 8 favorable outcomes out of 15. Therefore, the probability is $\frac{8}{15}$.

Question 16

Find the Probability of One Event or a Second Event Occurring
-One digit from the number 5,969,339 is written on each of seven cards. What is the probability of drawing a card that shows 5, 9, or 6?

Accepted Answer

The number 5,969,339 contains three different digits: 5, 9, and 6. The digit 5 appears once, 9 appears three times, and 6 appears twice, making a total of 6 cards out of 7 that show either 5, 9, or 6. Therefore, the probability is $\frac{6}{7}$, but since this option is not available, the correct interpretation of the question likely involves counting the distinct numbers (5, 9, 6) as the favorable outcomes, which are 3 out of the 7 digits, leading to a mistake in the provided options and explanation.

Question 17

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

It is impossible to roll a number that is both even and 5 on a 6-sided die. Therefore, the probability is 0.

Question 18

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

There are a total of 15 regions. Out of those, there are 7 even numbers (2, 4, 6, 8, 10, 12, and 14) and 5 multiples of 3 (3, 6, 9, 12, and 15). However, we need to be careful not to count the number 6 twice. Therefore, we subtract the number of even multiples of 3 (6 and 12), which leaves us with a total of 7+5-2=10 regions that meet the desired criteria. So the probability is 10/15, which simplifies to 2/3.

Question 19

Find the Probability of One Event and a Second Event Occurring
-If two 8-sided dice are rolled what is the probability that both numbers will be even?

Accepted Answer

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

Question 20

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 numbers less than 4 are 1, 2, and 3, which are three out of the six possible outcomes, making the probability $\frac{3}{6} = \frac{1}{2}$.

Quiz 8: Sequences, Induction, and Probability

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 -A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 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 -A card is drawn from a deck of 52 cards. What is the probability that it is a numbered card (2-10) or a heart?

Find the Probability of One Event or a Second Event Occurring -Give the probability that the roll of a die will show 6 or 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 diamond or that it is greater than 2 and less than 9?

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 1 or a spade?

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 that the card will have a value of 3 and be a face card?

Find the Probability of One Event or a Second Event Occurring -Given the sequence 3, 4, 5, 6 ... 42, what is the probability that a number in the sequence is even or that it is greater than 12 and less then 27?

Find the Probability of One Event or a Second Event Occurring -One digit from the number 4,696,336 is written on each of seven cards. What is the probability of drawing a card that shows 4 or 3?

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 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 4, 7, or 3?

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 7?

Find the Probability of One Event or a Second Event Occurring -One digit from the number 5,969,339 is written on each of seven cards. What is the probability of drawing a card that shows 5, 9, or 6?

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 8-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 -Give the probability that the roll of a die will show a number less than 4.

Quiz 8: Sequences, Induction, and Probability

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 -A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 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 -A card is drawn from a deck of 52 cards. What is the probability that it is a numbered card (2-10) or a heart?

Find the Probability of One Event or a Second Event Occurring -Give the probability that the roll of a die will show 6 or 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 diamond or that it is greater than 2 and less than 9?

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 1 or a spade?

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 - What is the probability that the arrow will land on 5 or 1 ?

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 that the card will have a value of 3 and be a face card?

Find the Probability of One Event or a Second Event Occurring -Given the sequence 3, 4, 5, 6 ... 42, what is the probability that a number in the sequence is even or that it is greater than 12 and less then 27?

Find the Probability of One Event or a Second Event Occurring -One digit from the number 4,696,336 is written on each of seven cards. What is the probability of drawing a card that shows 4 or 3?

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 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 4, 7, or 3?

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 7?

Find the Probability of One Event or a Second Event Occurring -One digit from the number 5,969,339 is written on each of seven cards. What is the probability of drawing a card that shows 5, 9, or 6?

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 8-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 -Give the probability that the roll of a die will show a number less than 4.