Question

events a and b are independent. p(a) = 0.3, and p(b) = 0.24. what is p(a and b)? write your answer as a decimal. do not round.

Explanation:

Step1: Recall the formula for independent events

For independent events \( A \) and \( B \), the probability of both \( A \) and \( B \) occurring is given by \( P(A \text{ and } B)=P(A)\times P(B) \).

Step2: Substitute the given values

We know that \( P(A) = 0.3 \) and \( P(B)=0.24 \). Substituting these values into the formula, we get \( P(A \text{ and } B)=0.3\times0.24 \).

Step3: Calculate the product

\( 0.3\times0.24 = 0.072 \).

Answer:

\( 0.072 \)