Mathematics 2012 JAMB Past Questions - Question 49: The probabilities that a student passes a Physics test is 2/3.if he takes three physics test,what is the probability that he passes two of the tests?

Correct Answer

A

Explanation

P = 2/3, F = 1/3T = P.P.F 2/3 X 2/3 X 1/3 = 4/27To find the probability that a student passes two out of three physics tests, we can use the concept of binomial probability.The probability that the student passes a physics test is 2/3, and the probability that he fails is 1/3.To calculate the probability of passing two out of three tests, we need to consider the different combinations in which this can occur.There are three possible scenarios:1. Pass, Pass, Fail2. Pass, Fail, Pass3. Fail, Pass, PassThe probability of passing two out of three tests in each scenario is given by:1. (2/3) * (2/3) * (1/3)2. (2/3) * (1/3) * (2/3)3. (1/3) * (2/3) * (2/3)To find the total probability, we sum up the probabilities of these three scenarios:(2/3) * (2/3) * (1/3) + (2/3) * (1/3) * (2/3) + (1/3) * (2/3) * (2/3)Simplifying this expression, we get:4/27 + 4/27 + 4/27 = 12/27 = 4/9Therefore, the probability that the student passes two out of three physics tests is 4/9.