Where Should You Take A Lost Salad - Gauthmath

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Question

P(B|A')= 7/10 P(A')= 3/8 P(B)= 2/5 Work out P(A∩ B). Give your answer as a fraction in its simplest form.SHOW LESS0

Solution

user avatar imageAnswer\(\frac{11}{80}\)ExplanationStep 1: Use the formula for conditional probability \( P(B|A') = \frac{P(A' \cap B)}{P(A')} \) to find \( P(A' \cap B) \). Given \( P(B|A') = \frac{7}{10} \) and \( P(A') = \frac{3}{8} \), calculate \( P(A' \cap B) \) as follows: \[ P(A' \cap B) = P(B|A') \cdot P(A') = \frac{7}{10} \cdot \frac{3}{8} = \frac{21}{80} \] Step 2: Use the fact that \( P(B) = P(A \cap B) + P(A' \cap B) \) to find \( P(A \cap B) \). Given \( P(B) = \frac{2}{5} \) and \( P(A' \cap B) = \frac{21}{80} \), calculate \( P(A \cap B) \) as follows: \[ P(A \cap B) = P(B) - P(A' \cap B) = \frac{2}{5} - \frac{21}{80} \] Step 3: To subtract the fractions, find a common denominator, which is 160. Convert \( \frac{2}{5} \) to \( \frac{64}{160} \) and \( \frac{21}{80} \) to \( \frac{42}{160} \). \[ P(A \cap B) = \frac{64}{160} - \frac{42}{160} = \frac{22}{160} \] Step 4: Simplify the fraction \( \frac{22}{160} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. \[ P(A \cap B) = \frac{11}{80} \] So, the probability of the intersection of events \( A \) and \( B \) is \( \frac{11}{80} \).Click to rate:37.7(77 votes)Search questionBy textBy image/screenshotDrop your file here orClick Hereto upload

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