A bag contains tickets numbered from 1 to 20. | vedclass

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Question

(A) The total number of tickets is $20$. The number of ways to draw $2$ tickets from $20$ is given by $^{20}C_2 = \frac{20 	imes 19}{2 	imes 1} = 19

Vedclass · Accepted Answer

$\frac{14}{95}$

Vedclass · Answer

(A) The total number of tickets is $20$. The number of ways to draw $2$ tickets from $20$ is given by $^{20}C_2 = \frac{20 	imes 19}{2 	imes 1} = 190$.The prime numbers between $1$ and $20$ are $2, 3, 5, 7, 11, 13, 17, 19$. There are $8$ such prime numbers.The number of ways to choose $2$ prime numbers from these $8$ prime numbers is given by $^8C_2 = \frac{8 	imes 7}{2 	imes 1} = 28$.The probability that both numbers are prime is $P = \frac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}} = \frac{28}{190}$.Simplifying the fraction,we get $P = \frac{14}{95}$.

$A$ bag contains tickets numbered from $1$ to $20$. Two tickets are drawn. The probability that both the numbers are prime,is

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