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14.Probability
medium
If out of $20$ consecutive whole numbers two are chosen at random, then the probability that their sum is odd, is
A
$\frac{5}{{19}}$
B
$\frac{{10}}{{19}}$
C
$\frac{9}{{19}}$
D
None of these
Solution
(b) The total number of ways in which $2$ integers can be chosen from the given $20$ integers ${}^{20}{C_2}.$
The sum of the selected numbers is odd if exactly one of them is given and one is odd.
$\therefore $ Favourable number of outcomes $ = {}^{10}{C_1} \times {}^{10}{C_1}$
$\therefore $ Required probability $ = \frac{{{}^{10}{C_1} \times {}^{10}{C_1}}}{{{}^{20}{C_2}}} = \frac{{10}}{{19}}.$
Standard 11
Mathematics
