Question

Problem Page At a certain college, 49% of the students are female, and 19% of the students major in civil engineering. Furthermore, 12% of the students both are female and major in civil engineering. (a) What is the probability that a randomly selected female student majors in civil engineering? Round your answer to 2 decimal places. (b) What is the probability that a randomly selected civil engineering major is female? Round your answer to 2 decimal places. g

Answer 1

Answer with Step-by-step explanation:

Let

A=Students are female

B=Students major in civil engineering

The probability that a students are female=P(A)=$\frac{49}{100}=0.49$

The probability that a student major in civil engineering=P(B)=$\frac{19}{100}=0.19$

The probability that students both are female=$P(A\cap B)=\frac{12}{100}=0.12$

a.We have to find the probability that a random selected female student major in civil engineering.

We have to find $P(B/A)$

$P(B/A)=\frac{P(A\cap B)}{P(A)}$

$P(B/A)=\frac{0.12}{0.49}=0.24$

Hence, the probability that a randomly selected female student majors in civil engineering=0.24

b.We have to find the probability that a random selected civil engineering major is female.

We have to find $P(A/B)$

$P(A/B)=\frac{P(A\cap B)}{P(B)}=\frac{0.12}{0.19}=0.63$

Hence, the probability that a randomly selected civil engineering major is female=0.63