Question
Question 3 Score: 0 of 1 point Given two independent events \( A \) and \( B \) with probabilities 0.694 and 0.148 respectively, what is the probability that both events occur? A 0.1027 B 0.0924 C 0.1232 D 0.113 E 0.0822
Ask by Gough Wells. in the United States
Feb 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that both events occur is approximately 0.1027, which is option A.
Solution
To find the probability that both events occur, multiply their probabilities because they are independent. That is:
P(A and B) = P(A) × P(B) = 0.694 × 0.148 ≈ 0.1027
So, the correct answer is A: 0.1027.
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Simplify this solution Beyond the Answer
To find the probability that both independent events \( A \) and \( B \) occur, you simply multiply their probabilities together. So, if \( P(A) = 0.694 \) and \( P(B) = 0.148 \), the calculation would be: \[ P(A \text{ and } B) = P(A) \times P(B) = 0.694 \times 0.148 \] Calculating that gives: \[ 0.694 \times 0.148 = 0.102592 \] Rounding this, we see that the closest answer is: **A 0.1027**.
