This Venn diagram shows sports played by 10 students.Let event A = The student plays basketball.Let event B = The student plays soccer.What is P(A|B)?A.B.C.D.

Break Down the Problem

1. Identify the total number of students and the number of students involved in both events A (basketball) and B (soccer).
2. Use the conditional probability formula to find $P(A|B)$.

Relevant Concepts

1. The formula for conditional probability is given by: $P(A|B) = \frac{P(A \cap B)}{P(B)}$ where:
   • $P(A|B)$ is the probability of event A occurring given that B has occurred.
   • $P(A \cap B)$ is the probability of both A and B occurring.
   • $P(B)$ is the probability of event B occurring.

Analysis and Detail

1. Total Students: 10
2. Find $P(A \cap B)$: Count the number of students that play both basketball and soccer from the Venn diagram.
3. Find $P(B)$: Count the number of students that play soccer.
4. Substitute these values into the conditional probability formula.

Verify and Summarize

1. Ensure the counts are accurate.
2. Recalculate $P(A|B)$ using the counts obtained.

Final Answer

Assuming from the diagram $P(A \cap B)$ is, for instance, 3 students and $P(B)$ is 5 students, we would have:

$P(A|B) = \frac{3}{5} = 0.6$

Please replace the values with the counts specifically from the Venn diagram provided for an accurate final answer.