Question

Two numbers are selected at random from the integers 1 to 9. If the sum is even, find the probability that both numbers are odd?

• A. $\frac{5}{8}$
• B. $\frac{3}{8}$
• C. $\frac{13}{204}$
• D. $Noneofthese$

Answer 1

The correct option is A $\frac{5}{8}$

There are 4 even numbers and 5 odd numbers
Let A = the event of choosing odd numbers
B = The event of getting the sum an even number.
Then $A\cap B$ = The event of choosing odd numbers whose sum is even
$\therefore n\left(B\right){=}^4{C}_2{+}^5{C}_2=16$
And $n(A\cap B){=}^5{C}_2=10$
$\therefore$ Required probability $=p\left(\frac{A}{B}\right)$
$=\frac{n(A\cap B)}{n\left(B\right)}=\frac{10}{16}=\frac{5}{8}$