probability and stats

Question

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

A	B	C	Total
Male	17	20	12	49
Female	2	3	15	20
Total	19	23	27	69

If one student is chosen at random,

find the probability that the student was male OR received a grade of "C". (Leave answer to four decimal places.)

After giving a test to a group of students, below are the summary of grades and gender.

Write as a reduced fraction.

A	B	C	Total
Male	3	8	13	24
Female	2	5	20	27
Total	5	13	33	51

If a student is randomly chosen, find the probability that the student did not earn an "C"

Answer 1

Hello Raquel,

In the first two way table, there are a total of 69 students, 49 of them are males, and 23 of them earned a C grade. Let event M = student is a male, and let event C = student earned a C. The question is asking to find the probability that the randomly selected student was a male OR earned a C. That is, find P(M or C).

According to the general addition rule, P(M or C) = P(M) + P(C) - P(M and C).

Since P(M) = 49/69, P(C) = 23/69, and P(M and C) = 20/69 (based on the values from the two way table)

It follows that P(M or C) = (49+23-20)/69 = 52/69 ≈ 0.7536

Similarly, in the second two way table there are 51 students and 13 earned a C. The question is asking for P(not earning a C) = 1 - P(C) by the complement rule. Hence, P(not earning a C) = 1 - 13/51 (don't forget to simplify your answer, that is write it as a reduced fraction).

Good Luck.