Question 1

Find the conditional probability.
-If two fair dice are rolled, find the probability that the numbers rolled form a "double" given that their sum is 11. 
A) 0
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 1 } { 3 }$

Accepted Answer

The answer of Find the conditional probability.
-If two fair dice...

Question 2

Find the conditional probability.
-If two cards are drawn at random without replacement from a standard deck, find P(ace on second|ace on first). 
A) $\frac { 1 } { 17 }$
B) $\frac { 4 } { 51 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 3 } { 52 }$

Accepted Answer

P(ace on second|ace on first) = P(ace on second) / P(ace on first) = 3/52 / 4/52 = 3/4 = 1/4

Question 3

An IRS auditor randomly selects 3 tax returns from 55 returns of which 10 contain errors. What is the probability that she selects none of those containing errors?
A)0.5409
B)0.5477
C)0.0046
D)0.006

Accepted Answer

The probability of selecting none of the returns containing errors can be calculated using combinations. There are 45 returns without errors out of 55. The number of ways to choose 3 returns from these 45 is 45C3. The total number of ways to choose any 3 returns from the 55 is 55C3. The probability is the ratio of these two combinations: (45C3) / (55C3) = 0.5409.

Question 4

Find the conditional probability.
-Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a queen is selected
B = event a diamond is selected. Determine $\mathrm { P } ( \mathrm { B } \mid \mathrm { A } )$.
A) $\frac { 1 } { 13 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 1 } { 52 }$

Accepted Answer

Given that a queen is selected (event A), there are 4 queens in a deck, and only 1 of them is a diamond. Thus, the probability of selecting a diamond given that a queen is selected is 1 out of 4 queens, which is $\frac{1}{4}$.

Question 5

Use the general multiplication rule to find the indicated probability.
-You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that both cards are black. 
A) $\frac { 13 } { 51 }$
B) $\frac { 25 } { 102 }$
C) $\frac { 1 } { 2652 }$
D) $\frac { 25 } { 51 }$

Accepted Answer

The probability of drawing a black card first is $\frac{26}{52}$ or $\frac{1}{2}$, since half of the 52 cards are black. After drawing one black card, there are now 51 cards left in the deck, with 25 of them being black. Thus, the probability of drawing a second black card is $\frac{25}{51}$. Using the general multiplication rule, the combined probability is $\frac{1}{2} \times \frac{25}{51} = \frac{25}{102}$.

Question 6

Find the conditional probability.
-If a single fair die is rolled, find the probability that the number rolled is 5 given that it is odd. 
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 1 } { 6 }$

Accepted Answer

Given that the die roll is odd, there are three possible outcomes: 1, 3, or 5. The probability that the outcome is specifically 5 among these three possibilities is $\frac{1}{3}$.

Question 7

A sample of 4 different calculators is randomly selected from a group containing 35 that are defective and 27 that have no defects. What is the probability that all four of the calculators selected
Are defective?
A)0.3541
B)2.9835
C)0.0939
D)0.1016

Accepted Answer

The probability of selecting 4 defective calculators out of a total of 62 (35 defective + 27 non-defective) is calculated using combinations. The probability is $\frac{{\binom{35}{4}}}{{\binom{62}{4}}}$, which simplifies to approximately 0.0939.

Question 8

Find the conditional probability.
-If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is a face card, given that the first card was a queen. 
A) $\frac { 4 } { 17 }$
B) $\frac { 3 } { 13 }$
C) $\frac { 5 } { 17 }$
D) $\frac { 11 } { 51 }$

Accepted Answer

The answer of Find the conditional probability.
-If two cards are...

Question 9

In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of
Rain on a day following a nonrainy day is 0.250. Find the probability of rain on three randomly
Selected consecutive days in January.
A)0.144
B)0.090
C)0.064
D)0.216

Accepted Answer

The probability of rain on three randomly selected consecutive days can be calculated by first determining the probability of rain on the first day, which is 0.400, then multiplying it by the probability of rain on the second day given that the first day was rainy, which is 0.600, and finally multiplying that result by the probability of rain on the third day given that the second day was rainy, which is again 0.600. Therefore, the calculation is 0.400 * 0.600 * 0.600 = 0.144.

Question 10

Find the conditional probability.
-If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is a spade, given that the first card was a spade.
A) $\frac { 11 } { 51 }$
B) $\frac { 4 } { 17 }$
C) $\frac { 3 } { 13 }$
D) $\frac { 1 } { 4 }$

Accepted Answer

After drawing the first spade, there are 51 cards left in the deck, 12 of which are spades. So, the probability that the second card drawn is a spade is $\frac{12}{51} = \frac{4}{17}$.

Question 11

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability that both marbles are white. 
A) $\frac { 3 } { 28 }$
B) $\frac { 9 } { 56 }$
C) $\frac { 3 } { 8 }$
D) $\frac { 3 } { 32 }$

Accepted Answer

The probability of drawing a white marble on the first draw is 3/8. The probability of drawing a white marble on the second draw is 2/7. The probability of drawing both marbles white is (3/8) * (2/7) = 3/28.

Question 12

What is the probability that 4 randomly selected people all have different birthdays?
A)0.9891
B)0.9836
C)0.9729
D)0.9918

Accepted Answer

The probability that 4 randomly selected people all have different birthdays, assuming each day is equally likely and ignoring leap years, is calculated by considering the total number of favorable outcomes over the total possible outcomes. For the first person, any birthday is possible (365/365). For the second person, to have a different birthday, there are 364 options out of 365. For the third, 363 options, and for the fourth, 362 options. Thus, the probability is (365/365) * (364/365) * (363/365) * (362/365) = 0.9836.

Question 13

Find the conditional probability.
-If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is red, given that the first card was a heart. 
A) $\frac { 26 } { 51 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 25 } { 52 }$
D) $\frac { 25 } { 51 }$

Accepted Answer

Given that the first card drawn is a heart, it means one red card is already taken out from the deck, leaving 51 cards in total. Since half of a standard deck is red (26 cards) and one red card (a heart) has been removed, there are now 25 red cards left. Therefore, the probability that the second card drawn is red is 25 out of the remaining 51 cards, which is $\frac{25}{51}$.

Question 14

Use the general multiplication rule to find the indicated probability.
-You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen. 
A) $\frac { 13 } { 102 }$
B) $\frac { 2 } { 13 }$
C) $\frac { 4 } { 663 }$
D) $\frac { 1 } { 663 }$

Accepted Answer

The probability of drawing a king first is $\frac{4}{52}$ since there are 4 kings in a deck of 52 cards. After drawing a king, there are 51 cards left, and the probability of drawing a queen next is $\frac{4}{51}$ since there are 4 queens in the remaining deck. Using the general multiplication rule, the combined probability is $\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = \frac{4}{663}$.

Question 15

Find the conditional probability.
-If three cards are drawn at random without replacement from a standard deck, find the probability that the third card is a face card, given that the first card was a queen and the second card was a 5. 
A) $\frac { 6 } { 25 }$
B) $\frac { 3 } { 13 }$
C) $\frac { 11 } { 50 }$
D) $\frac { 1 } { 5 }$

Accepted Answer

The answer of Find the conditional probability.
-If three cards are...

Question 16

In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of
Rain on a day following a nonrainy day is 0.250.
Find the probability that January 1st and January 2nd are rainy and that January 3rd and 4th are
Not rainy given that December 31st was clear all day.
A)0.024
B)0.038
C)0.045
D)0.072

Accepted Answer

The answer of In January in a certain city the...

Question 17

A bag contains 8 red chips and 5 blue chips. Two chips are selected randomly without replacement from the bag. What is the probability that the two chips are the same color?
A)0.513
B)0.571
C)0.359
D)0.487

Accepted Answer

The answer of A bag contains 8 red chips and...

Question 18

Find the conditional probability.
-If two fair dice are rolled, find the probability that the sum is 6 given that the roll is a "double". 
A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 5 }$
D) $\frac { 1 } { 6 }$

Accepted Answer

The answer of Find the conditional probability.
-If two fair dice...

Question 19

Two cards are selected without replacement from a standard deck of 52 cards. What is the probability that both cards are the same color (i.e., either both black or both red)?
A)0.490
B)0.500
C)0.250
D)0.245

Accepted Answer

The probability that both cards are the same color can be calculated by considering the probability of drawing two black cards plus the probability of drawing two red cards. There are 26 black cards and 26 red cards in a standard deck of 52 cards. The probability of drawing two black cards is (26/52) * (25/51), and the probability of drawing two red cards is (26/52) * (25/51). Adding these probabilities gives 2 * (26/52) * (25/51) = 0.490.

Question 20

Find the conditional probability.
-Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a diamond is selected
B = event a club is selected. Determine $\mathrm { P } ( \mathrm { A } \mid$ | (not $\mathrm { B } ) )$.
A) $\frac { 1 } { 3 }$
B) 1
C) 0
D) $\frac { 1 } { 4 }$

Accepted Answer

The probability of selecting a diamond given that a club is not selected is $\frac{13}{39}$, because there are 13 diamonds out of the remaining 39 cards (52 cards total minus the 13 clubs), which simplifies to $\frac{1}{3}$.

Quiz 11: Probability

Find the conditional probability. -If two fair dice are rolled, find the probability that the numbers rolled form a "double" given that their sum is 11.

Find the conditional probability. -If two cards are drawn at random without replacement from a standard deck, find P(ace on second|ace on first) .

An IRS auditor randomly selects 3 tax returns from 55 returns of which 10 contain errors. What is the probability that she selects none of those containing errors?

Find the conditional probability. -Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a queen is selected B = event a diamond is selected. Determine $\mathrm { P } ( \mathrm { B } \mid \mathrm { A } )$ .

Use the general multiplication rule to find the indicated probability. -You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black.

Find the conditional probability. -If a single fair die is rolled, find the probability that the number rolled is 5 given that it is odd.

A sample of 4 different calculators is randomly selected from a group containing 35 that are defective and 27 that have no defects. What is the probability that all four of the calculators selected Are defective?

Find the conditional probability. -If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is a face card, given that the first card was a queen.

Find the conditional probability. -If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is a spade, given that the first card was a spade.

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability that both marbles are white.

What is the probability that 4 randomly selected people all have different birthdays?

Find the conditional probability. -If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is red, given that the first card was a heart.

Use the general multiplication rule to find the indicated probability. -You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen.

Find the conditional probability. -If three cards are drawn at random without replacement from a standard deck, find the probability that the third card is a face card, given that the first card was a queen and the second card was a 5.

A bag contains 8 red chips and 5 blue chips. Two chips are selected randomly without replacement from the bag. What is the probability that the two chips are the same color?

Find the conditional probability. -If two fair dice are rolled, find the probability that the sum is 6 given that the roll is a "double".

Two cards are selected without replacement from a standard deck of 52 cards. What is the probability that both cards are the same color (i.e., either both black or both red) ?

Find the conditional probability. -Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a diamond is selected B = event a club is selected. Determine $\mathrm { P } ( \mathrm { A } \mid$ | (not $\mathrm { B } ) )$ .