Q. The probability that a student passes a statistics test is 2/3 and the probability that he passes both statistics and mathematics is
14/45. The probability that he passes at least one test is 4/5. What
is the probability that the student passes the mathematics test?

4/9 or 44.44%

Step-by-step explanation:

We have the following probabilities:

Probability of winning the statistical test = P (s) = 2/3

Probability of winning the mathematics and statistics test = P (s n m) = 14/45

Probability of winning at least one test = P (s u m) = 4/5

We have that, the probability of winning the mathematics test P (m) can be found in the following way:

P (s n m) = P (s) + P (m) - P (s u m)

replacing we have:

14/45 = 2/3 + P (m) - 4/5

P (m) = 14/45 - 2/3 + 4/5

p (m) = 4/9 = 0.444

Which is the same as there is a 44.44% probability that I will win the math test