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?

Question

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ChiKesselman ChiKesselman · Answer 1 · 2020-04-23T07:23:57+02:00

Answer:

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

Step-by-step explanation:

We are given the following in the question:

Percentage of students that have green eyes = 65%

[tex]P(G) =0.65[/tex]

Percentage of students that have red hairs = 25%

[tex]P(R) =0.25[/tex]

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

[tex]P(G\cap R) =0.15[/tex]

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

[tex]P(R|G) = \dfrac{P(R\cap G)}{P(G)}[/tex]

Putting values, we get,

[tex]P(R|G)=\dfrac{0.15}{0.65} = 0.2307\approx 23\%[/tex]

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