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Given that events A and B are independent with
P(A)=0.79 and
P(B)=0.6, determine the value of
P(A and
B), rounding to the nearest thousandth, if necessary.
Answer:

Given that events A and B are independent with $P(A)=0.79$ and $P(B)=0.6$ , determine the value of $P(A$ and $B)$ , 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)=0.79

and

P(B)=0.6

, determine the value of

P(A

and

B)

, rounding to the nearest thousandth, if necessary.

\newline

Answer:

Understand independent events: Understand the concept of independent events. For two independent events $A$ and $B$ , the probability of both events occurring is the product of their individual probabilities. This is expressed as $P(A \text{ and } B) = P(A) \times P(B)$ .
Calculate $P(A \text{ and } B)$ : Use the given probabilities to calculate $P(A \text{ and } B)$ . We are given $P(A) = 0.79$ and $P(B) = 0.6$ . To find $P(A \text{ and } B)$ , we multiply these probabilities together. $P(A \text{ and } B) = P(A) \times P(B) = 0.79 \times 0.6$
Perform multiplication: Perform the multiplication to find the probability of both events occurring. $\newline$ $P(A \text{ and } B) = 0.79 \times 0.6 = 0.474$
Round the result: Round the result to the nearest thousandth if necessary. $\newline$ The result $0.474$ is already to the nearest thousandth, so no further rounding is needed.

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