Question

Two coins are tossed once. Find P(A/B) in each of the following:

A = Tail appears on one coin, B = One coin shows head.

Answer 1

When two coins are tossed, total outcomes are

{HH, HT, TH, TT} = 4

A = Tail appears on one coin= {HT, TH} = 2

Probability of A = P(A) = \(\cfrac24=\cfrac12\)

B= One coin shows head ={HT, TH} = 2

Probability of B = P(B) = \(\cfrac24=\cfrac12\)

(A ∩ B) = one coin shows head and another shows tail = {HT, TH} = 2

P (A ∩ B) = \(\cfrac24=\cfrac12\)

Hence, \(P(\cfrac{A}{B})=\cfrac{P(A\cap B)}{P(B)}\)