Two numbers are selected simultaneously from the set {6, 7, 8, 9, ……, 39}. If the sum of selected numbers is even then the probability that both the selected numbers are odd, is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option 4: $\frac{1}{2}$
Total numbers from 6 to 39 = 34 numbers
- Even numbers = 17
- Odd numbers = 17
A : Sum of selected numbers is even.
B : Selected numbers are odd.
$P(A)=\frac{{ }^{17} C_2+{ }^{17} C_2}{{ }^{34} C_2}, P(A \cap B)=\frac{{ }^{17} C_2}{{ }^{34} C_2}$
$P(B ~|~ A)=\frac{P(A \cap B)}{P(A)}=\frac{{ }^{17} C_2}{{ }^{17} C_2+{ }^{17} C_2}$
=$\frac{136}{272}$
=$\frac{1}{2}$