(A) The total number of ways to select $2$ tickets from $20$ is given by $n = \binom{20}{2} = \frac{20 \times 19}{2 \times 1} = 190$. The prime number

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(A) The total number of ways to select $2$ tickets from $20$ is given by $n = \binom{20}{2} = \frac{20 \times 19}{2 \times 1} = 190$. The prime numbers between $1$ and $20$ are $2, 3, 5, 7, 11, 13, 17, 19$. There are $8$ such numbers. The number of ways to select $2$ prime numbers from these $8$ is $r = \binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28$. The probability of the event is $P = \frac{r}{n} = \frac{28}{190} = \frac{14}{95}$.

Class 11 Mathematics Probability Permutation and Combination based Probability

Medium

Two tickets are drawn at random from tickets numbered $1$ to $20$. The probability that the numbers on both tickets are prime numbers is ..........

A
$\frac{14}{95}$
B
$\frac{7}{95}$
C
$\frac{1}{95}$
D
$\frac{13}{95}$

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Two tickets are drawn at random from tickets numbered $1$ to $20$. The probability that the numbers on both tickets are prime numbers is ..........

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