This question meant to help with the notion of condilinal probabiy anid rando va

Question

This question meant to help with the notion of condilinal probabiy anid rando varible nolalion. Suppose air cois lussed. Define lhe randuTm varlable X to be 1 If the outcome is talls and 0 If the outcnme is heads. I 1, tnss an unfair coin where the prahability of gelling lails is 0.1. I X D, luss lhe sarne fair coin. Now define a second random vanable Xas ollows: he oulce l lhe second coiri loss is N- Iil the oulcome of the second coin loss is talls. X- Olf the outcome of the second coln toss Is heads Calculate PX2 0) round answers ta the nearest 4th decimal place it needed

Explanation / Answer

P(X2 =0) = (Both cases when (X1=0 , X2=0) and (X1=1,X2=0) )

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

= 0.55

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

= ( 1/2 * 0.6 ) / 0.55

= 0.5455 Answer

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