Question

Form a group of 5 men and 3 women to form a committee of 4 person at random. find the probability that :-
(1) it contains 2 men and 2 women
(2)it contains majority of men
(3)it contains majority of women ​

Answer 1

Answer:

1. 1
2. 5/4
3. 3/4is the probablities

Answer 2

Concept

The number of favorable outcomes to all possible outcomes of an event is the ratio, which is known as probability. The number of good outcomes can be represented by the symbol x for an experiment with 'n' number of outcomes. The following equation can be used to determine an event's probability.

Probability (Event) = Positive Outcomes/Total Outcomes = x/n

Given

group of 5 men and 3 women, a committee of 4 persons is formed.

Find

the probability that the committee contains:

• 2 men and 2 women
• majority of men
• majority of women

Solution

(i) total men = 5

probability that the  committee contains 2 men = 2/5

total women = 3

probability that the  committee contains 2 men = 2/3

probability that the committee contains both men and women = 2/5 +2/3

= 6+10/15

= 16/15

(ii) majority of men

p(3m∩w) = p(3m).p(w)

= 5C₃×3C₁/8C₄

= 1/2

(iii) majority of women

p(3w∩m) =  p(3w).p(m)

=3C₃ × 5C₁/8C₄

= 1/14

Hence we get the required answers.

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