Question

A card is drawn from a deck of 52 playing cards. Given that it is a black card, what is the probability that it is the following? (Enter your probabilities as fractions.)

(a) a club


(b) a jack

A card is drawn from a deck of 52 playing cards. Find the following probabilities as fractions.

Find the following probabilities.

Pr(queen ∩ red)	=
Pr(red)	=
Pr(queen | red)	=

(b) Find the following probabilities.

What is the probability that the drawn card is a queen given that it is a red card?

A bag contains 5 red balls and 7 white balls. Two balls are drawn without replacement. (Enter your probabilities as fractions.)

(a) What is the probability that the second ball is white, given that the first ball is red?


(b) What is the probability that the second ball is red, given that the first ball is white?


(c) Answer part (a) if the first ball is replaced before the second is drawn.

Three construction companies have bid for a job. Max knows that the two companies with which he is competing have probabilities 1/5 and 1/9, respectively, of getting the job. What is the probability that Max will get the job? (Enter your probability as a fraction.)

A die has been "loaded" so that the probability of rolling any even number is

5

27

and the probability of rolling any odd number is

4

27

. (Assume the die is six-sided with each side numbered one through six.)

(a)

Find the following probabilities. Enter your probabilities as fractions.

Pr(2 ∩ even)	=
Pr(even)	=
Pr(2 | even)	=

What is the probability of rolling a 2, given that an even number is rolled?

(b)

Find the following probabilities. Enter your probabilities as fractions.

Pr(3 ∩ (3 or 6))	=
Pr(3 or 6)	=
Pr(3 | (3 or 6))	=

What is the probability of rolling a 3, given that a number divisible by 3 is rolled?

A red ball and 5 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting each of the following? (Enter your probabilities as fractions.)

(a) a red ball on the first draw and a white ball on the second


(b) 2 white balls


(c) 2 red balls

To test its shotgun shells, a company fires 5 of them. What is the probability that all 5 will fire properly if 6% of the company's shells are actually defective? (Round your answer to four decimal places.)

Three construction companies have bid for a job. Max knows that the two companies with which he is competing have probabilities 1/5 and 1/9, respectively, of getting the job. What is the probability that Max will get the job? (Enter your probability as a fraction.)

Answer 1

1.

Given that it is a black card P(B) = 26

P(a club) = 13/26

(In 52 deck of cards 26 are black and 26 are red cards. In black 13 are club and remaining are leaf)

P(a jack) = 2/26

(Jack has 4 cards 2 are red and 2 black)

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