# There Are Three Boys and Two Girls. a Committee of Two is to Be Formed. Find the Probability of Events that the Committee Contains - Algebra

Sum

There are three boys and two girls. A committee of two is to be formed. Find the probability of events that the committee contains :
a) At least one girl.
b) One boy and one girl
c) Only boys

#### Solution

Let,
the three boys be b1, b2, b3 and
the two girls be g1 and g2.

A committee of two is to be formed.
The Sample space(S) is
S = {(b1, b2), (b1, b3), (b1,g1), (b1, g2), (b2, b3), (b2, g1), (b2, g2),
(b3 , g1), (b3, g2), (g1, g2)}
⇒ n(S)=10

a) Let B be event that the committee contains only one girls.
B = { (b1,g1), (b1, g2), (b2, g1), (b2, g2), (b3 , g1), (b3, g2), (g1, g2)}
⇒ n(B) = 7

P(B)=(n(B))/(n(S))=7/10

b) Let C be the event that the committee contains one boy and one girl.
C = { (b1,g1), (b1, g2), (b2, g1), (b2, g2), (b3 , g1), (b3, g2)}
⇒ n(C)=6

P(C)=(n(C))/(n(S))=6/10 = 3/5

c) Let D be the event that the committee contains only boys.
D = { (b1, b2), (b1, b3), (b2, b3) }
⇒ n(D) = 3

P(D)=(n(D))/(n(S))=3/10

Concept: Basic Ideas of Probability
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