Question

the probability that a student passes statistics is 2/3 and the probability that he asses english is 4/9. if the probability of passing at least one course is 4/5, what is the probability of his passing both the courses

Answer 1

The probability of the student passing both statistics and English is 22/27.

How to find the probability ?

Since the student can only either pass both courses or not pass both courses, the sum of these probabilities must be 1.

Probability of not passing both:

Probability of not passing statistics = 1 - 2/3

= 1/3

Probability of not passing English = 1 - 4/9

= 5/9

Probability of not passing both courses (P(not both)) = (1/3) * (5/9)

= 5/27

Probability of passing both:

P(not both) + P(both) = 1

P(both) = 1 - P(not both) = 1 - (5/27)

= 22/27