Question

Two fair dice are rolled simultaneously. It is found that one of the dice show odd prime number. The probability that the remaining dice also show an odd prime number, is equal to

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

Answer 1

The correct option is A $\frac{1}{5}$

Odd prime on a die are 3 and 5.
Let event A = one of the dice show odd prime number, and event B = remaining dice also shows odd prime number.
$P\left(\frac{B}{A}\right)=\frac{n(A\bigcap B)}{n\left(A\right)}.A=\left\{\right(3,1\left)\right(3,2),(3,3),(3,4),(3,5),(3,6),(5,1),...(5,6),(1,3),(2,3),...(6,3),(1,5),...(5,5),\}AndA\bigcap B=\left\{\right(3,3).(5,5),(3,5\left)\right(5,3\left)\right\}\therefore P\left(\frac{A}{B}\right)=\frac{4}{20}=\frac{1}{5}.$