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Given that events A and B are independent with
P(A)=0.72 and
P(B)=0.1, determine the value of
P(A nn B), rounding to the nearest thousandth, if necessary.
Answer:

Given that events A and B are independent with $P(A)=0.72$ and $P(B)=0.1$ , determine the value of $P(A \cap B)$ , rounding to the nearest thousandth, if necessary. $\newline$ Answer:

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Identify independent events

Full solution

Q. Given that events A and B are independent with

P(A)=0.72

and

P(B)=0.1

, determine the value of

P(A \cap B)

, rounding to the nearest thousandth, if necessary.

\newline

Answer:

Understand concept of independent events: Understand the concept of independent events. For independent events $A$ and $B$ , the probability of both events occurring together, denoted as $P(A \cap B)$ , is the product of their individual probabilities. $P(A \cap B) = P(A) \times P(B)$
Substitute given probabilities into formula: Substitute the given probabilities into the formula. $\newline$ $P(A) = 0.72$ $\newline$ $P(B) = 0.1$ $\newline$ $P(A \cap B) = 0.72 \times 0.1$
Calculate product to find $P(A \cap B)$ : Calculate the product to find $P(A \cap B)$ . $P(A \cap B) = 0.72 \times 0.1 = 0.072$
Round result if necessary: Round the result to the nearest thousandth if necessary. $\newline$ The result is already at the thousandth place, so no further rounding is needed.

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