Question

2 students given a english test. The probability of student A passing the test is 0.95 while the probability of student B is 0.8 :

a) probability of both pass the exam
b) exactly one student pass the exam
c) at least one student pass the exam​

Answer 1

a) The probability of both students passing the exam is the product of their individual probabilities of passing the exam:

P(A passes and B passes) = P(A passes) × P(B passes) = 0.95 × 0.8 = 0.76

b) The probability of exactly one student passing the exam can be calculated as the sum of the probabilities of A passing and B failing, and the probability of A failing and B passing:

P(A passes and B fails) + P(A fails and B passes) = (0.95 × 0.2) + (0.05 × 0.8) = 0.19

c) The probability of at least one student passing the exam is the complement of the probability that both students fail the exam:

P(at least one student passes) = 1 - P(A fails and B fails) = 1 - (0.05 × 0.2) = 0.99

Therefore, the probability of at least one student passing the exam is 0.99.