Question

Two dice are thrown. The probability that the sum of the 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. $None$

Answer 1

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

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