What is the probability that the freshman had less than 2 incorrect answers?

Question

The following chart shows the number of questions that incoming freshmen got incorrect on a mathematics placement test along with the associated frequencies:

Number wrong Frequency

0 325

1 240

2 170

3 122

4 85

5 45

6 10

7 or more 3

A freshman is picked at random.

b) What is the probability that the freshman had at least 1 incorrect answer?

c) What is the probability that the freshman had at most 3 incorrect answers?

Answer 1

Add up all the frequencies to get the total number of frequencies.

The probability that the freshman had at least 1 incorrect answer = 1 - probability the freshman had no incorrect answers = 1 - (0 frequencies /total number of frequencies) = 1 - (325/total number of frequencies)

The probability that the freshman had at most 3 incorrect answers = sum (0, 1, 2, 3 frequencies)/total number of frequencies = (325 + 240 + 170 + 122)/total number of frequencies.