Question

The guidance department has reported that of the senior class, 7.8% are members of key club, K, 8.6% are enrolled in AP Physics, P, and 6.7% are in both. 1) Determine the probability of P given K, to the nearest tenth of a percent. 2) The principal would like a basic interpretation of these results. Write a statement relating your calculated probabilities to student enrollment in the given situation.

Answer 1

the probability of P given K is 0.86

Explanation:

Conditional probability is defined as the probability that an event would happen based on the occurrence of an event that has already happened. It is calculated by multiplying the probability of the both the preceding event and the succeeding event together. It is given by the formula:

`P(B/A)=(P(A nB))/(P(A))`

Given that:

Probability of members in the key club P(K) = 7.8% = 0.078

Probability of members enrolled in AP physics P(P) = 8.6% = 0.086

Probability of members in both P(P n K) = 6.7% = 0.067

Therefore:

`P(P/K)=(P(PnK))/(P(K)) =(0.067)/(0.078) = 0. 86`

the probability of P given K is 0.86