Question

In a certain college, $4$% of men and $1$% of women are taller than $1.6$m. Also. $60$% of students are women. If a student selected at random is found to be taller than $1.6$m. then the probability that the student being a woman is

• A. $\frac{3}{11}$
• B. $\frac{5}{11}$
• C. $\frac{6}{11}$
• D. $\frac{8}{11}$

Answer 1

The correct option is A $\frac{3}{11}$

Let total number of students be 1000

60% are girls & 40% are boys

600 students are girls & 400 students are boys

4% of boys are taller than 1.6m

No. of boys taller than 1.6m=4%of400=16

1% of girls are taller than 1.6m

No. of girls taller than 1.6m=1%of600=6

One student is selected at random probability that it is a girl=$\frac{P(G>1.6)}{P(G>1.6)+P(B>1.6)}=\frac{6/1000}{6/1000+16/1000}=6/22=3/11$