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Given
P(A)=0.72,P(B)=0.3 and
P(A or
B)=0.754, find the value of
P(A and
B), rounding to the nearest thousandth, if necessary.
Answer:

Given $P(A)=0.72, P(B)=0.3$ and $P(A$ or $B)=0.754$ , find the value of $P(A$ and $B)$ , rounding to the nearest thousandth, if necessary. $\newline$ Answer:

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Find trigonometric functions using a calculator

Full solution

Q. Given

P(A)=0.72, P(B)=0.3

and

P(A

or

B)=0.754

, find the value of

P(A

and

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 and B), we can use the formula that relates the probabilities of A, B, and their union (A or B): $\newline$ $P(A \text{ and } B) = P(A) + P(B) - P(A \text{ or } B)$
Substitution: Now we substitute the given probabilities into the formula: $\newline$ $P(A \text{ and } B) = 0.72 + 0.3 - 0.754$
Calculation: Perform the calculation: $\newline$ $P(A \text{ and } B) = 1.02 - 0.754$ $\newline$ $P(A \text{ and } B) = 0.266$ $\newline$ Since we are asked to round to the nearest thousandth if necessary, our answer is already at that precision.

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