Question

A teacher has found that the probability that a student studies for a test is 0.610.61​, and the probability that a student gets a good grade on a test is 0.790.79​, and the probability that both occur is 0.560.56. a. Are these events​ independent? b. Given that a student​ studies, find the probability that the student gets a good grade. c. Given that a student gets a good​ grade, find the probability that the student studied.

Answer 1

Answer with step-by-step explanation:

Let

A=Student studies for a test

B=Student gets good grade on a test

The probability that a student studies  for  a test=P(A)=0.61

The probability that a student gets   a good grade on a test=P(B)=0.79

The probability that both occur=$P(A\cap B)=0.56$

a.We have to find the events are independent

We know that if two events A and B are independent then

$P(A)\cdot P(B)=P(A\cap B)$

$P(A)\cdot P(B)=0.61\times 0.79=0.4819$

$P(A\cap B)\neq P(A)\cdot P(B)$

Hence, given events are not independent.

b.We have to find $P(B/A)$

$P(B/A)=\frac{P(A\cap B)}{P(A)}$

$P(B/A)=\frac{0.56}{0.61}=0.92$

c. We have to find $P(A/B)$

$P(A/B)=\frac{P(A\cap B}{P(B)}$

$P(A/B)=\frac{0.56}{0.79}=0.71$