Question

Unattempted question 10 expand previous next check 0/2 ptsretries 3reattempts 98 A test was given to a group of students. The grades and residency are summarized below.

a b c total
In-state 2 3 5 10
Out-of-state 20 7 18 45
Total 22 10 23 55
If one student is chosen at random from those who took the test, find the probability that the student was out-of-state given they got a c. Write your answer as a reduced fraction.
✕P (out-of-state ∣ c) = _______.

Answer 1

The probability that a student was out-of-state given they got a C is 18/23. This is calculated using the number of out-of-state students who got a C divided by the total number of students who got a C.

Step-by-step explanation:

To find the probability that a student was out-of-state given they got a C, you need to use conditional probability. The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B), where P(A|B) is the probability of event A given event B has occurred, P(A ∩ B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.

From the question, we are given the following data in terms of number of students:

• Number of out-of-state students who got a C = 18
• Total number of students who got a C = 23

Therefore, we can calculate the conditional probability as follows:

P(out-of-state | C) = Number of out-of-state students who got a C / Total number of students who got a C

P(out-of-state | C) = 18 / 23

The reduced fraction for 18/23 cannot be further simplified, so the final answer is:

P(out-of-state | C) = 18/23