There are three boys and two girls. A committee of two is to be formed, find the probability of events that the committee contains :

7. There are three boys and two girls. A committee of two is to be formed, find the probability of events that the committee contains :

(i) at least one girl

(ii) one boy and one girl

(iii) only boys 

Sol. Let three boys be denoted as B1, B2, B3 and two girls be denoted as G1, G2. A committee of two can be formed in the following ways

∴  S = { B1 B2, B1 B3, B1 G1, B1 G2, B2 B3, B2 G1, B2 G2, B3 G1, B3 G2, G1 G2 }

∴  n (S) = 10

(i) Let A be event that committee contains atleast one girl

A = { B1 G1, B1 G2, B2 G1, B2 G2, B3 G1, B3 G2, G1 G2 }

n (A) = 7

P (A) = n (A)/n (S)

∴  P (A) = 7/10

(ii) Let B be the event that committee contains one boy and one girl

B = { B1 G1, B1 G2, B2 G1, B2 G2, B3 G1, B3 G2 }

n (B) = 6

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

∴  P (B) = 6/10

∴  P (B) = 3/5

(iii)Let C be the event that committee contain only boys

C = { B1 B2, B1 B3, B2 B3 }

n (C) = 3

P (C) = n (C)/n (S)

∴  P (C) = 3/10

There are three boys and two girls. A committee of two is to be formed, find the probability of events that the committee contains at least one girl.

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:

Since a committee of two is be formed from three boys and two girls,

Sample Space = { B1B2, B1B3, B1G1, B1G2, B2B3, B2G1, B2G2, B3G1, B3G2, G1G2} a. Let A = Event of forming a committee which contains atleast one girl A = { B1G1, B1G2, B2G1, B2G2, B3G1, B3G2, G1G2} n(A) = 7 P(A) = n(A) = 7 n(S) 10 b. Let B = Event that the committee contains one boy and one girl. B = { B1G1, B1G2, B2G1, B2G2, B3G1, B3G2, } ∴ n(B) = 6 P(B) = n(B) = 6 = 3 n(S) 10 5 c. Let C = Event that the committee contains only boys. C = { B1B2, B1B3, B2B3} ∴ n(C) = 3 P(C) = n(C) = 3 = 3 n(S) 10 10