Given P(A)=0.6,P(B)=0.39 and P(A uu B)=0.646, find the value of P(A nn B), rounding to the nearest thousandth, if necessary. Answer:

Formula Application: To find the probability of the intersection of two events A and B, denoted as P(A ∩ B), we can use the formula: P(A ∩ B) = P(A) + P(B) - P(A ∪ B)Substitution: Now, let's plug in the given values into the formula: P(A ∩ B) = 0.6 + 0.39 - 0.646Calculation: Perform the calculation: P(A ∩ B) = 0.99 - 0.646 P(A ∩ B) = 0.344Final Answer: Since the problem asks for the answer rounded to the nearest thousandth, we do not need to round further as our answer is already to three decimal places.

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Given
P(A)=0.6,P(B)=0.39 and
P(A uu B)=0.646, find the value of
P(A nn B), rounding to the nearest thousandth, if necessary.
Answer:

Given $P(A)=0.6, P(B)=0.39$ and $P(A \cup B)=0.646$ , find the value of $P(A \cap B)$ , rounding to the nearest thousandth, if necessary. $\newline$ Answer:

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Full solution

Q. Given

P(A)=0.6, P(B)=0.39

and

P(A \cup B)=0.646

, find the value of

P(A \cap B)

, rounding to the nearest thousandth, if necessary.

\newline

Answer:

Formula Application: To find the probability of the intersection of two events $A$ and $B$ , denoted as $P(A \cap B)$ , we can use the formula: $\newline$ $P(A \cap B) = P(A) + P(B) - P(A \cup B)$
Substitution: Now, let's plug in the given values into the formula: $\newline$ $P(A \cap B) = 0.6 + 0.39 - 0.646$
Calculation: Perform the calculation: $\newline$ $P(A \cap B) = 0.99 - 0.646$ $\newline$ $P(A \cap B) = 0.344$
Final Answer: Since the problem asks for the answer rounded to the nearest thousandth, we do not need to round further as our answer is already to three decimal places.