Question

A pair of dice is thrown simultaneously, find the probability that the sum is obtained 9 when there is an odd number on the first die.___

• A. $\frac{1}{9}$
• B. $\frac{1}{2}$
• C. $\frac{2}{36}$
• D. $\frac{4}{9}$

Answer 1

The correct option is A $\frac{1}{9}$

Let A be the event of getting a sum of 9 and B be the event of getting an odd number on the first die.
$\therefore A\left\{\right(3,6\left)\right(4,5),(5,4\left)\right(6,3\left)\right\}B=(1,1),(1,2),(1,3)...(3,1),(3,2),(3,3)...(5,1),(5,2)...(5,6)P\left(A\right)=\frac{4}{36}=\frac{1}{9}andP\left(B\right)=\frac{18}{36}=\frac{1}{2}$
$\therefore P\left(\frac{A}{B}\right)=$ Probability of occurence of A when B occurs
$\Rightarrow P\left(\frac{A}{B}\right)=$ Probability of getting 9 as the sum when there is an odd number on first die.
$\Rightarrow P\left(\frac{A}{B}\right)=\frac{n(A\cap B)}{n\left(B\right)}=\frac{2}{18}=\frac{1}{9}\left[Here\right(A\cap B)=(3,6),(6,3\left)\right]$