Question

two events, a and b, are independent. if $p(a) = 0.3$ and $p(b) = 0.2$, what is $p(a \text{ and } b)$?

Explanation:

Step1: Recall the formula for independent events

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

Step2: Substitute the given values

We are given that \( P(A) = 0.3 \) and \( P(B) = 0.2 \). Substituting these values into the formula, we get:
\( P(A \text{ and } B) = 0.3 \times 0.2 \)

Step3: Perform the multiplication

Calculating the product: \( 0.3 \times 0.2 = 0.06 \)

Answer:

\( 0.06 \)