Question

A fair coin is flipped 3 times. Events A and B are defined as: A: There are at least two consecutive heads somewhere in the sequence. B: The last flip comes up tails. What is p(B | A)?

Answer 1

Solution:

Given: A fair coin is flipped 3 times.

Sample Space S is:

S = { HHH, HHT , HTH , THH , TTH , THT, HTT , TTT }

n(S) = number of outcomes of S = 8

A : There are at least two consecutive heads somewhere in the sequence.

A : { HHH, HHT , THH }

n(A) = number of outcomes of A = 3

Thus

P(A) = n(A) / n(S)

B : The last flip comes up tails.

B : { HHT,  THT, HTT , TTT }

n(B) = number of outcomes of B = 4

thus

A and B : {HHT }

thus

n(A and B) = number of outcomes of both A and B = 1

We have to find:

P( B | A) = .......?

Using conditional probability formula:

where

P( A and B) = n(A and B) / n(S)

P( A and B) = 1 / 8

P( A and B) = 0.125

and

P(A) = n(A) / n(S)

P(A) = 3 / 8

P(A) = 0.375

thus