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# A Bag Contains Tickets Numbered from 1 to 20. Two Tickets Are Drawn. Find the Probability That Both the Tickets Have Prime Numbers on Them - Mathematics

A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that  both the tickets have prime numbers on them

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#### Solution

Clearly, the sample space is given by S = {1, 2, 3, 4, 5,...19, 20}.
∴ n(S) = 20C2 = 190

Let E1 be the event where both the tickets have prime numbers on them.
Then E1 = {2, 3, 5, 7, 11, 13, 17, 19}
∴ Favourable number of ways = n(E1) = 8C2
Hence, required probability = P(E1) = $\frac{n\left( E_1 \right)}{n\left( S \right)} = \frac{^{8}{}{C}_2}{^{20}{}{C}_2} = \frac{14}{95}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 40.1 | Page 48
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