Question
Suppose that events \( E \) and \( F \) are independent. In addition, possible \( P(E)=0.45 \) and \( P(F)=0.2 \). What is \( P(E \) and \( F) \) ? \( P(E \) and \( F)=\square \) (Simplify your answer. Do not round.)
Ask by Peters Ortiz. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( P(E \text{ and } F) = 0.09 \)
Solution
To find \( P(E \text{ and } F) \) for independent events, we use the formula:
\[
P(E \text{ and } F) = P(E) \times P(F)
\]
Given that \( P(E) = 0.45 \) and \( P(F) = 0.2 \), we have:
\[
P(E \text{ and } F) = 0.45 \times 0.2 = 0.09
\]
Thus, the answer is:
\[
P(E \text{ and } F) = 0.09
\]
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Simplify this solution Extra Insights
When two events \( E \) and \( F \) are independent, the probability of both events occurring, denoted \( P(E \text{ and } F) \), is given by the product of their individual probabilities. Thus, you can use the formula: \[ P(E \text{ and } F) = P(E) \times P(F) \] Plugging in the given values: \[ P(E \text{ and } F) = 0.45 \times 0.2 = 0.09 \] So, \[ P(E \text{ and } F) = 0.09 \]
