how do I solve this step by step and what is the final answer

Question

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

A	B	C	Total
Male	18	9	8	35
Female	13	14	3	30
Total	31	23	11	65

If one student is chosen at random,

Find the probability that the student did NOT get an "C" Write your answer as a fraction.

  

Answer 1

Hi May,

You want the probability that the student did not get a C. To get this, you can use the complement rule. First, look at the table for the number of students who DID get a C. This is 23. Now, you were not asked about gender, so we can ignore that. Next, you need the total number of students. This is 65. So, probability that student got a C is:

P(C)=23/65

Now, complement rule implies that if 23 students of 65 got Cs, then (65-23) students did not. Thus:

P(non-C)= (65-23)/65

P(non-C)=42/65

I hope this helps.