A fair die is rolled and a coin is flipped If the result is

A fair die is rolled and a coin is flipped. If the result is greater than 4, a fair coin is flipped, and otherwise, an unfair coin with P [ H ] = 2 / 3 is flipped.

(a) Find the probability of heads.

(b) Find the probability of tails.

(c) Find the probability that the die roll was greater than 4 if a heads was flipped.

(d) Find the probability that the die roll was a 1 if a heads was flipped.

Solution

A) THE PROBABILITY OF HEADS =

WHEN NUMBER LESS THEN 4 = 2/3*1/2 = 1/3

WHEN NUMBER GREATER THEN 4 = 1/3*1/2 = 1/6

B)PROBABILITY OF TAILS

WHEN NUMBER LESS THEN 4 = 1 - 1/3 = 2/3

WHEN NUMBER GREATER THEN 4 = 1-1/6 = 5/6

C) PROBABILITY THAT DIE WAS GREATER THN 4 = (1/6)/(1/2) = 1/3 AS HERE P(A INTERSECTION B)/ P(B) WILL BE USED AND THE VALUES OF THIS ARE TAKEN FROM ABOVE

D) = (1/6*1/2)/(1/2) = 1/6 SAME FORMULA USED AS IN PART C