Question

at any given time, the probability that there are at least twenty students in the school gym is 0.3. the probability that there are at least twenty students in the school gym and that at least one of them is a freshman is 0.12. what is the probability that there is at least one freshman in the school gym given that there are at least twenty students in the gym? 0.036 0.12 0.4 0.42

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Let $A$ be the event that there is at least one freshman in the school gym, and $B$ be the event that there are at least twenty students in the gym.

Step2: Identify given probabilities

We are given that $P(B) = 0.3$ and $P(A\cap B)=0.12$.

Step3: Calculate the conditional probability

Substitute the values into the formula: $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.12}{0.3}$.
$P(A|B) = 0.4$

Answer:

C. 0.4