Question

100 POINTS!!! A group of students were asked if they carry a credit card. The responses are listed in the table. If a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. Round your answer to three decimal places.

Answer 1

21/100=.21

Since it’s saying their is a student selected at random that means it is out of 100 students. Then it’s asking for freshman who have a credit card which is 21 people. That means it’s 21/100 which is .21 probability.

Answer 2

0.350 (3 d.p.)

Explanation:

`\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)`

Let P(A) = probability that the student is a freshman

Let P(B) = probability that the student owns a credit card

Use the given table to calculate the probability that the student is a freshman:

`\implies \sf P(A)=(60)/(100)=0.6`

And the probability that the student is a freshman and owns a credit card:

`\implies \sf P(A \cap B)=(21)/(100)=0.21`

To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of B given A is:

`\sf P(B|A)=(P(A \cap B))/(P(A))`

Substitute the found values into the formula:

`\implies \sf P(B|A)=(0.21)/(0.6)=0.35`

Therefore, the probability that the student owns a credit card given that they are a freshman is 0.35