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14.Probability
easy
In a lottery $50$ tickets are sold in which $14$ are of prize. A man bought $2$ tickets, then the probability that the man win the prize, is
A
$\frac{{17}}{{35}}$
B
$\frac{{18}}{{35}}$
C
$\frac{{72}}{{175}}$
D
$\frac{{13}}{{175}}$
Solution
(a) In $50$ tickets $14$ are of prize and $36$ are blank.
Number of ways both the tickets are blank $ = {}^{36}{C_2}$
Thus the probability of not winning the prize $ = \frac{{{}^{36}{C_2}}}{{{}^{50}{C_2}}} = \frac{{18}}{{35}}$.
Hence probability of winning the prize $ = 1 – \frac{{18}}{{35}} = \frac{{17}}{{35}}.$
Standard 11
Mathematics
