a committee of 5 persons is to be selected randomly from a group of 5men & 10women. find the probability that committee consists of 2men & 3women . and find the probability of the committe consists of all women.
Answers
The probability that the committee consists of 2 men & 3 women is 0.399
The probability of the committee consisting of all women is 3.33 × 10^-4
Given: A committee of 5 persons is to be selected randomly from a group of 5 men & 10 women
To Find:
(1) the probability that the committee consists of 2 men & 3 women.
(2) The probability of the committee consists of all women.
Solution:
(1) Total number of people = 5 + 10 = 15
Total men = 5 and total women = 10
So, number of ways to select 2 men and 3 women is
= 5 C 2 × 10 C 3
= 1200
Total number of ways of selecting 5 out of 15 people is,
= 15 C 5
= 3003
Now, the required probability is ,
= 1200 / 3003
= 0.399
(2) Total number of people = 5 + 10 = 15
Total men = 5 and total women = 10
So, number of ways to select 5 women is
= 5 C 5
= 1
Total number of ways of selecting 5 out of 15 people is,
= 15 C 5
= 3003
Now, the required probability is ,
= 1 / 3003
= 3.33 × 10^-4
Hence,
The probability that the committee consists of 2 men & 3 women is 0.399
The probability of the committee consisting of all women is 3.33 × 10^-4
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Concept:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
Given:
A committee of 5 persons is to be selected randomly from a group of 5 men & 10 women
To Find:
(1) the probability that the committee consists of 2 men & 3 women.
(2) The probability of the committee consists of all women.
Solution:
(1) Total number of people = 5 + 10 = 15
Total men = 5 and total women = 10
So, number of ways to select 2 men and 3 women is
= ⁵C₂ × ¹⁰C₃
= 1200
Total number of ways of selecting 5 out of 15 people is,
= ¹⁵C₅
= 3003
Now, the required probability is ,
= 1200 / 3003
= 0.399
(2) Total number of people = 5 + 10 = 15
Total men = 5 and total women = 10
So, number of ways to select 5 women is
= ⁵C₅
= 1
Total number of ways of selecting 5 out of 15 people is,
= ¹⁵C₅
= 3003
Now, the required probability is ,
= 1 / 3003
= 3.33 × 10^-4
Hence,
The probability that the committee consists of 2 men & 3 women is 0.399
The probability of the committee consisting of all women is 3.33 × 10^-4
#SPJ2