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,
[tex] P(s) = \frac{82}{500} = \bold{0.164} [/tex]
[tex] P(p) = \frac{73}{500} = \bold{0.146} [/tex]
[tex] P(b) = \frac{42}{500} = \bold{0.084} [/tex]
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
