probability chosen at random

Question

Giving a test to a group of students, the grades and gender are summarized below

A	B	C	Total
Male	19	5	7	31
Female	2	13	10	25
Total	21	18	17	56

If one student is chosen at random,

Find the probability that the student was male OR got an "A".

Answer 1

Since there are 31 male students out of a total of 56 students, the probability that a student was a male is:

P(Male) = 31/56 = 0.554

Likewise, there were 21 A's out of a total of 56 grades on the test, so the probability that a student got an A is:

P(A) = 21/56 = 0.375

We also need to count the number of males who received A's:

P(A and Male) = 19/56 = 0.339

We need to subtract this probability from the total probability of males and A's to get the correct answer:

P(Male OR A) = P(Male) + P(A) - P(Male AND A)

= 0.554 + 0.375 - 0.339

= 0.59

I hope this helps!