Events E and F are independent.  If P(E) is 0.85, and P(F) is 0.4, then P(E and F) =

1. Break Down the Problem

We need to find the probability of the intersection of two independent events E and F, denoted as P(E and F).

2. Relevant Concepts

For independent events, the probability of both events occurring is given by the formula: $P(E \text{ and } F) = P(E) \times P(F)$

3. Analysis and Detail

Given:

• $P(E) = 0.85$
• $P(F) = 0.4$

Using the formula for independent events, we can substitute the values:

$P(E \text{ and } F) = 0.85 \times 0.4$

4. Verify and Summarize

Now, calculating the product:

$P(E \text{ and } F) = 0.85 \times 0.4 = 0.34$

Final Answer

The probability $P(E \text{ and } F)$ is $0.34$.