(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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Class 11

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Probability

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Permutation and Combination based Probability

Twenty tickets are marked with the numbers $1, 2, \dots, 20$. If three tickets are drawn at random,what is the probability that the tickets marked $7$ and $11$ are among them?

Easy

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The probability that the sum of $2$ numbers chosen at random from $30$ consecutive integers is odd is..........

Easy

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If two numbers are chosen at random from $1, 2, 3, \dots, 100$ and multiplied,what is the probability that the product is divisible by $3$?

Medium

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If out of $20$ consecutive whole numbers two are chosen at random,then the probability that their sum is odd,is

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Two cards are drawn from a pack of $52$ cards. What is the probability that at least one of the cards drawn is an ace?

Easy

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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?

Similar Questions

Twenty tickets are marked with the numbers $1, 2, \dots, 20$. If three tickets are drawn at random,what is the probability that the tickets marked $7$ and $11$ are among them?

The probability that the sum of $2$ numbers chosen at random from $30$ consecutive integers is odd is..........

If two numbers are chosen at random from $1, 2, 3, \dots, 100$ and multiplied,what is the probability that the product is divisible by $3$?

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