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

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