Let A and B be events with Pr [B] doesnt\'t equal 0. Then the probability of A g

Question

Let A and B be events with Pr [B] doesnt't equal 0. Then the probability of A given B written Pr [A | B] , is

Pr[A | B]  = Pr [ A and B]   /   Pr [B]

Use this formula to solve each of the following:

a) Two fair dice are rolled and the numbers on the uppermost faces noted. Determine the probability that one die shows a 4, given that the sum of the numbers is 7.

b) An urn contains red balls marked 1, 2, 3 a white ball marked 4, and blue balls marked 5, 6, 7, 8, 9 and a ball is selected at random. Determine the probability that it is red, fiven that the ball is known to have an even number.

c) A single card is drawn from a standard deck of 52 cards and replaced by a joker, and then a second card is drawn. What is the probability that both cards are aces?

Explanation / Answer

part a)event A=4 is needed on the face of a dice

event B=a total of 7

Pr(B)=(6/36)

favorable cases are {(3,4),(4,3)}

total case{(4,3),(3,4),(6,1),(1,6),(5,2),(2,5)}

Pr(A|B)=(2/6)

so answer=(1/3)

part b) A=ball is red

B=ball is even numbered

Pr(A|B)=(1/4) ANSWER

part c) probability=(4/52)*(3/52)

ANSWER=0.00444

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