Question

10. there are two boys and three girls a committee of two is to be formed. find the probability that the
commmittee contain (1) 1 girl [2] 1 boy and 1 girl (3] oniy boys (4) at least one girl.​

Answer 1

Step-by-step explanation:

Step by step solution is enclosed.

Answer 2

Given,

• There are two boys and three girls.

• A Committee of two is to be formed

To find,

The probability that the committee contains,

1. 1 boy and 1 girl

2. Only boys

3. At least one girl.​

Solution,

Number of ways we can make a committee of two from two boys and three girls = $^{5}C_{2} = 10$

[ The combination function represents the number of possible pairs that can be formed given a certain number of distinct bodies. ]

$^{n}C_{r} = \frac{n!}{(n - r)!r!}$

Part 1,

Number of ways we can choose one girl = $^{3}C_{1} = 3$

(We can choose any of the three girls for the committee, therefore, three choices)

Number of ways we can choose one boy = $^{2}C_{1} = 2$

(There are two boys, we have two choices, either the first one or the second)

P(1 girl and 1 boy) = $\frac{2*3}{10} = \frac{6}{10} = 0.6$

Part 2,

Number of ways we can choose two boys = $^{2}C_{2} = 1$

(When we choose both the boys, it's just one possible way to do that)

P(2 boys) = $\frac{1}{10} = 0.1$

Part 3,

At least one girl in the committee means, there has to be a minimum of girls in the committee, in some cases, there can be two as well.

We calculate it by subtracting the probability of cases with no girl in the committee from the total probability of 1.

P(at least one girl) = 1 - P(no girls)

                              = $1 - 0.1 = 0.9$