Probability Ques 25
Question-
When a student was selected from a class consisting of 25 girls and a certain number of boys, the probability of the student being a boy is $\frac{3}{8}$. If 2 students were selected from this class, what will be the probability of exactly one girl and one boy being selected?
(1) $\frac{25}{52}$
(2) $\frac{23}{52}$
(3) $\frac{27}{52}$
(4) $\frac{21}{52}$
(5) $\frac{29}{52}$
(Canara Bank PO Exam 04.03.2018)
Show Answer
Correct Answer: (1)
Solution: (1)
Number of boys in the class $=x$
Probability of selecting 1 boy $=\frac{x}{x+25}$
$\therefore \frac{x}{x+25}=\frac{3}{8}$
$\Rightarrow 8 x=3 x+75$
$\Rightarrow 5 x=75 $
$\Rightarrow x=\frac{75}{5}=15$
When 2 students are selected, Total possible outcomes $={ }^{40} C_{2}=\frac{40 \times 39}{2}=780$
Favourable outcomes $={ }^{15} C_{1} \times{ }^{25} C_{1}$ $=15 \times 25=375$
$\therefore$ Required probability $=\frac{375}{780}=\frac{25}{52}$
BETA
