There are 8 boys and 6 girls in a class. If two students are selected at random from the class, find the probability that they are of (a) the same sex ; (b)...

Assessment: WAEC SSCE - Further Mathematics - 2015 (Essay) Subject: Further Mathematics

Question 1 Report

There are 8 boys and 6 girls in a class. If two students are selected at random from the class, find the probability that they are of

(a) the same sex ;

(b) different sex.

Answer

Answer Details

8 boys and 6 girls; two students chosen at random.

Total ways to choose 2 from 14:

\[{}^{14}C_2=\frac{14\times 13}{2}=91\]

(a) Same sex.

\[{}^{8}C_2+{}^{6}C_2=\frac{8\times7}{2}+\frac{6\times5}{2}=28+15=43\]\[P(\text{same sex})=\frac{43}{91}\]

(b) Different sex.

\[{}^{8}C_1\times{}^{6}C_1=8\times6=48\]\[P(\text{different sex})=\frac{48}{91}\]

(Check: \(\dfrac{43}{91}+\dfrac{48}{91}=1\).)

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