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

Answer:

0.350  (3 d.p.)

Step-by-step explanation:

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

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:

$\implies \sf P(A)=\dfrac{60}{100}=0.6$

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

$\implies \sf P(A \cap B)=\dfrac{21}{100}=0.21$

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:

$\sf P(B|A)=\dfrac{P(A \cap B)}{P(A)}$

Substitute the found values into the formula:

$\implies \sf P(B|A)=\dfrac{0.21}{0.6}=0.35$

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