In a city school, 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair. What is the probability (rounded to the nearest whole percent) that a randomly selected student will have dark hair, given that the student has blue eyes?

Hint:

P (A|B) = P (A∩B) / P (B)

46%

43%

21%

67%

The correct answer option is 43%.

Step-by-step explanation:

We are given that 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair.

We are to find the probability of a student getting selected will have dark hair with blue eyes.

P (D|B) = P (D∩B) / P (B)

Substituting the given values in it to get:

P (D|B) = 0.3 / 0.7 = 0.428

Rounding it to the nearest whole percent we get:

0.428 * 100 = 42.8% ≈ 43%