Question

A fair die is thrown until a score of less than five points is obtained. The probability of obtaining less than three points on the last throw is

• A. $\frac{3}{4}$
• B. $\frac{4}{5}$
• C. $\frac{5}{6}$
• D. $\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2}$

A = number less than five points
= {1, 2, 3, 4}
And B = numbers less than three points
= {1, 2}
$\therefore A\cap B=\{1,2\}$
$\therefore n\left(A\right)=4,n\left(B\right)=2$ and $n(A\cap B)=2$
Hence,$P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}$
$=\frac{n(A\cap B)}{n\left(A\right)}$
$=\frac{2}{4}=\frac{1}{2}$