Question

Two coins are tossed once. Let $A=$ Tail appears on one coin $B=$ coin show Head. Find $P\left(A|B\right)$.

Answer 1

Given that two coins are tossed once. Let head be denoted by $h$ and tails by $t$

Possible outcomes are $:-$

$S=(h,h),(h,t),(t,h),(t,t)$

We need to find the probability that tails appears on one coin, if we know that tails appears on one coin, if we know that one coin shows head.

Let $A:$ One coin shows head

$B:$ Tail appears on one coin

We need to find $P\left(A|B\right)$

$A=(h,t),(t,h)$

$B=(h,t),(t,h)$

$\Rightarrow P\left(A\right)=P\left(B\right)=\frac{2}{4}=\frac{1}{2}$

Now, $P\left(A|B\right)=\frac{P(A\cap B)}{P\left(B\right)}$

$=\frac{\frac{1}{2}}{\frac{1}{2}}$

$=1$