Answer:
0.383 (3 d.p.)
Step-by-step explanation:
Probability formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Let P(A) = probability that the student owns a credit card
Let P(B) = probability that the student is a freshman
Use the given table to calculate the probability that the student is a freshman and owns a credit card:
[tex]\implies \sf P(B \cap A)=\dfrac{23}{100}=0.23[/tex]
Use the given table to calculate the probability that the student is a freshman:
[tex]\sf \implies P(B) = \dfrac{60}{100}=0.6[/tex]
To find the probability that the student owns a credit card given that they are a freshman, use the conditional probability formula:
Conditional Probability Formula
The probability of A given B is:
[tex]\sf P(A|B)=\dfrac{P(B \cap A)}{P(B)}[/tex]
Substitute the found values into the formula:
[tex]\implies \sf P(A|B)=\dfrac{0.23}{0.6}=0.383333...[/tex]
Therefore, the probability that the student owns a credit card given that they are a freshman is 0.383 (3 d.p.).
