Question

How are your grades? In a recent semester at a local university, students enrolled in both Statistics and Psychology . Of these students, got an A in statistics, got an A in psychology, and got an A in both statistics and psychology. Round the answers to four decimal places, as needed.

Answer 1

Question:

How are your grades?

In a recent semester at a local university, 500 students enrolled in both Statistics and Psychology. Of these students, 82 got an A in statistics, 73 got an A in psychology, and 42 got an A in both statistics and psychology.

a) Find the probability that a randomly selected student got an A in Statistics or Psychology or in both.

b) Find the probability that a randomly selected student did not get an A in Psychology.

Round the answers to four decimal places, as needed.

Answer:

a) 0.226

b) 0.854

Step-by-step explanation :

Given:

Total number of students= 500

Number of A in statistics = 82

Number of A in psychology =73

Number of A in both = 42

a) To find the probability that a randomly selected student got an A in Statistics or Psychology or both.

Let's use the formula :

P(s) + P(p) - p(b)

P(s) = probability of students that got A in statistics

P(p) = probability of students that got A in psychology

P(b) = probability of students that got A in both

Where,

$P(s) = \frac{82}{500} = \bold{0.164}$

$P(p) = \frac{73}{500} = \bold{0.146}$

$P(b) = \frac{42}{500} = \bold{0.084}$

Therefore,

P(s) + P(p) - p(b)

= 0.164 + 0.146 - 0.084

= 0.226

Probability that a randomly selected student got an A in Statistics or Psychology or in both = 0.226

b) The probability that a randomly selected student did not get an A in Psychology.

Here we use the formula :

1 - P(p)

We already know P(p) = 0.146

Therefore, 1 - P(p) =

1 - 0.146

= 0.854

The probability that a randomly selected student did not get an A in Psychology = 0.854