(A) Total number of ways to select $2$ people from $13$ is given by $n(S) = {}_{13}C_2 = \frac{13 \times 12}{2 \times 1} = 78$. Let $A$ be the event t

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(A) Total number of ways to select $2$ people from $13$ is given by $n(S) = {}_{13}C_2 = \frac{13 \times 12}{2 \times 1} = 78$. Let $A$ be the event that at least one woman is selected. The number of ways to select at least one woman is: $n(A) = ({}_5C_1 \times {}_8C_1) + ({}_5C_2 \times {}_8C_0) = (5 \times 8) + (10 \times 1) = 40 + 10 = 50$. Therefore,the probability $P(A) = \frac{n(A)}{n(S)} = \frac{50}{78} = \frac{25}{39}$.

Class 11 Mathematics Probability Permutation and Combination based Probability

Medium

$A$ total of $13$ people,consisting of $5$ women and $8$ men,have applied for a job. If $2$ people are to be selected from these $13$ people,what is the probability that at least one woman is selected?

A
$25/39$
B
$14/39$
C
$5/13$
D
$10/13$

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Probability

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Permutation and Combination based Probability

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$A$ total of $13$ people,consisting of $5$ women and $8$ men,have applied for a job. If $2$ people are to be selected from these $13$ people,what is the probability that at least one woman is selected?

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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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