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)=
`(49)/(100)=0.49`

The probability that a student major in civil engineering=P(B)=
`(19)/(100)=0.19`

The probability that students both are female=
`P(A\cap B)=(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)=(P(A\cap B))/(P(A))`

`P(B/A)=(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)=(P(A\cap B))/(P(B))=(0.12)/(0.19)=0.63`

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