Question

Two dice are thrown. The probability that the sum of numbers coming up on them is 9, if it is known that the number 5 always occurs on the first die, is

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

Answer 1

The correct option is A $\frac{1}{6}$

let A = event that 5 comes on the first dice
$\therefore$ A = {(5,1), (5,2),....,(5,6) and let B = event that sum on both dice is 9
$A\bigcap B=(5,4)\therefore P\left(\frac{B}{A}\right)=\frac{n(A\bigcap B)}{n\left(A\right)}=\frac{1}{6}.$