Question

Consider the experiment of tossing a coin.If the coin shows tail,toss it again but if shows head,then throw a die.Find the conditional probability of the event that 'the die shows a number greater than 3' given that 'there is at least one head'.

Answer 1

Let E:Die shows a number greater than 3 and F: there is at least one head.
$\Rightarrow E:\{H4,H5,H6\},F:\{HT,H1,H2,H3,H4,H5,H6\}\therefore P\left(F\right)=1-\frac{1}{4}=\frac{3}{4},P(E\cap F)=\frac{3}{12}=\frac{1}{4}\therefore P\left(E|F\right)=\frac{P(E\cap F)}{P\left(F\right)}=\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{1}{3}$