Question

Ina city school, 65% of students have green eyes. 25% have red hair, and 15% have green eyes and

red hair. What is the probability (rounded to the nearest whole percent) that a randomly selected

student will have red hair given that the student has green eyes?

Answer 1

23% of student will have red hair given that the student has green eyes.

Explanation:

We are given the following in the question:

Percentage of students that have green eyes = 65%

`P(G) =0.65`

Percentage of students that have red hairs = 25%

`P(R) =0.25`

Percentage of students that have green eyes and red hairs = 15%

`P(G\cap R) =0.15`

We have to find the conditional probability of randomly selected student that will have red hair given that the student has green eyes.

`P(R|G) = (P(R\cap G))/(P(G))`

Putting values, we get,

`P(R|G)=(0.15)/(0.65) = 0.2307\approx 23\%`

Thus, 23% of student will have red hair given that the student has green eyes.