Question

A coin is tossed twice, where E : Tail appear on one coin and F : one coin shows head. Find P(E/F).

Answer 1

The sample space for two coins tossed one time is S=(HH,HT,TH,TT). The number of total outcomes in 4.

Given E: Tail appears on one coin, E=(HT,TH). The total number of outcomes is 2.

⇒P(E)=Number of favorable outcomes in ETotal number of outcomes in S=2/4=1/2

Given F: one coin shows head, F=(HT,TH). The total number of outcomes is 2.

⇒P(F)=Number of favorable outcomes in FTotal number of outcomes in S=2/4=1/2

For our set of events E∩F=(HT,TH). Total number of outcomes = 2.

⇒P(E∩F)=Number of favorable outcomesTotal number of outcomes in S=2/4=1/2

Given P(E), P(F), P(E ∩ F), P(E/F) =P(E∩F)/P(F)

⇒P(E∩F)/P(F)=1/2 / 1/2 = 1.