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— You are here If P(A)=0.8,P(B)=0.5 and P(B∣A)=0.4, find (i) P(A nn B) Given P(A)=0.8,P(B)=0.5&P(B∣A)=0.4 Now,

— You are here\newlineIf P(A)=0.8,P(B)=0.5 P(A)=0.8, P(B)=0.5 and P(B∣A)=0.4 P(B \mid A)=0.4 , find\newline(i) P(A∩B) P(A \cap B) \newlineGiven\newlineP(A)=0.8,P(B)=0.5&P(B∣A)=0.4 P(A)=0.8, P(B)=0.5 \& P(B \mid A)=0.4 \newlineNow,

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Full solution

Q. — You are here\newlineIf P(A)=0.8,P(B)=0.5 P(A)=0.8, P(B)=0.5 and P(B∣A)=0.4 P(B \mid A)=0.4 , find\newline(i) P(A∩B) P(A \cap B) \newlineGiven\newlineP(A)=0.8,P(B)=0.5&P(B∣A)=0.4 P(A)=0.8, P(B)=0.5 \& P(B \mid A)=0.4 \newlineNow,
  1. Understand formula and relationship: Step 11: Understand the formula for conditional probability and the relationship between P(A)P(A), P(B)P(B), and P(B∣A)P(B|A).P(B∣A)=P(A∩B)P(A)P(B|A) = \frac{P(A \cap B)}{P(A)}Now, rearrange to find P(A∩B)P(A \cap B):P(A∩B)=P(B∣A)×P(A)P(A \cap B) = P(B|A) \times P(A)
  2. Substitute given values: Step 22: Substitute the given values into the rearranged formula. \newlineP(A∩B)=0.4×0.8P(A \cap B) = 0.4 \times 0.8
  3. Perform multiplication: Step 33: Perform the multiplication to find P(A∩B)P(A \cap B).\newlineP(A∩B)=0.32P(A \cap B) = 0.32

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