Out of 40 consecutive integers two integers are drawn at random. The probability that their sum is odd is

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$\frac{40}{39}$

$\frac{25}{29}$

$\frac{20}{39}$

$\frac{15}{29}$

answer is B.

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Detailed Solution

$(S) = {}^{40}{C_{2}}$

E=Sum is odd

$\begin{array}{rcl} n (E) & = & {}^{20}{C_{1} \times {}^{20}{C_{1}}} \end{array}$

$\begin{array}{rcl} P (E) & = & \frac{20 \times 20}{{}^{40}{C_{2}}} \end{array}$

$\begin{array}{rcl} P (E) & = & \frac{20 \times 20 \times 2}{40 \times 39} = \frac{20}{39} \end{array}$

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