This question is mean lo help wilh ine noion of condtionai p

This question is mean! lo help wilh ine noion of condtionai probability end random varieble notation. Suppose a fair coin is tossed. Define the random ariahle Atn b1 if the outcome is tails and 0 it the outcome Is heads. If Xi 1, toss an unfalr coln where the probablity of getting a tails is 0.4. If X1 D toss the same fair cui. Now deie secornd rand variuble Xs follows. x, = if the outcome of the second coin toss is tails. -i the autcome of the second oin tss is hcads Calculate P(XX1) (round answers to the nearest 4th decimal place If needed)

Solution

P(X1 =1 ) = 1/2

P(X2 =0 / X1 =1) = P( X1 = 1 AND X2 = 0) / P (X1 = 1)

= ( 1/2 * 0.6 ) / (1/2)

= 0.6 Answer