Question

A coin is tossed twice and the four possible outcomes are assumed to be equally likely. If A is the event, 'both head and tail have appeared' and B the event,' at most one tail is observed,' then the value of P(B/A) is ______.

Options

• 1

• 2

• ${\displaystyle \frac{1}{2}}$

• ${\displaystyle \frac{1}{4}}$

Answer 1

A coin is tossed twice and the four possible outcomes are assumed to be equally likely. If A is the event, 'both head and tail have appeared' and B the event,' at most one tail is observed,' then the value of P(B/A) is 1.

Explanation:

P(A) = ${\displaystyle \frac{2}{4}}$ = ${\displaystyle \frac{1}{2}}$

P(B) = ${\displaystyle \frac{3}{4}}$

${\displaystyle P\left(\frac{B}{A}\right)=\frac{P(B\cap A)}{P\left(A\right)}=\frac{\frac{1}{2}}{\frac{1}{2}}}$ = 1