enmobladatn
2022-07-20
Answered

What is the addition rule for mutually exclusive events?

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taguetzbo

Answered 2022-07-21
Author has **16** answers

If events A and B are mutually exclusive of each other, then:

$P\left(A\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}B\right)=P\left(A\right)+P\left(B\right)$

Mutually exclusive means that A and B cannot occur at the same time, which means P(A and B) = 0.

For example, with a single six-sided die, the probability that you roll a "4" in a single roll is mutually exclusive of rolling a "6" on that same roll because a single die can only show 1 number at a time.

In this example, if event A is rolling a "6" and event B is rolling a "4", then P(A) = 1/6 and P(B) = 1/6, and the addition rule for these two mutually exclusive events is:

$\frac{1}{6}+\frac{1}{6}=\frac{1}{3}$

Thus, the addition of these two events equals $\frac{1}{3}$

$P\left(A\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}B\right)=P\left(A\right)+P\left(B\right)$

Mutually exclusive means that A and B cannot occur at the same time, which means P(A and B) = 0.

For example, with a single six-sided die, the probability that you roll a "4" in a single roll is mutually exclusive of rolling a "6" on that same roll because a single die can only show 1 number at a time.

In this example, if event A is rolling a "6" and event B is rolling a "4", then P(A) = 1/6 and P(B) = 1/6, and the addition rule for these two mutually exclusive events is:

$\frac{1}{6}+\frac{1}{6}=\frac{1}{3}$

Thus, the addition of these two events equals $\frac{1}{3}$

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