First slide

Theorems of probability

Question

Two integers are selected at random from integers 1 to 11. If the sum is even then the probability that both numbers are odd is

Moderate

A

$\frac{6}{11}$
B

$\frac{3}{5}$
C

$\frac{2}{5}$
D

$\frac{4}{5}$

Solution

Sum even = both even or both odd
$n (A) = 5_{C_{2}} + 6_{C_{2}}$

$n (A \cap B) = 6_{C_{2}}$

$P (B / A) = \frac{n (A \cap B)}{n (A)}$

$= \frac{6_{C_{2}}}{5_{C_{2}} + 6_{C_{2}}}$

$= \frac{15}{10 + 15} = \frac{3}{5}$

Required Probability is $\frac{3}{5}$

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