For two mutually exclusive events A and B, compute P ( A ∪ B ) P\left(A\cup B\right) P ( A ∪ B ) if P ( A ) = 0.15 P\left(A\right)=0.15 P ( A ) = 0.15 and P ( B ) = 0.32 P\left(B\right)=0.32 P ( B ) = 0.32

In this problem, we're asked for two mutually exclusive events, a and b. What is the probability of a or b if the probability of a is 0.15 and the probability of b is 0.32? Now this is a really specific type of problem because they're just explicitly giving us all of the information that we need. We don't even know what our events are, and we don't have to calculate their probabilities because they're just given to us. So all we need to do here is plug this into our formula. We know for two mutually exclusive events, the probability of a or b happening is simply equal to the probability of a is 0.32. So plugging these values in and adding them together I get the probability of A or B happening is equal to 0.47. So that's our final answer here. Thanks for watching and I'll see you in the next one.

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4. Probability

Addition Rule

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4. Probability

Addition Rule

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Multiple Choice

For two mutually exclusive events A and B, compute $P\left(A\cup B\right)$ if $P\left(A\right)=0.15$ and $P\left(B\right)=0.32$

$0.048$

$0.17$

$0.47$

$0.53$

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Verified step by step guidance

Understand that for two mutually exclusive events A and B, the probability of their union, P(A ∪ B), is simply the sum of their individual probabilities because they cannot occur simultaneously.

Write down the formula for the probability of the union of two mutually exclusive events: P(A ∪ B) = P(A) + P(B).

Substitute the given probabilities into the formula: P(A ∪ B) = 0.15 + 0.32.

Perform the addition to find the probability of the union of events A and B.

Verify that the calculated probability is one of the provided options to ensure the solution is correct.

5:14m

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Struggling with Statistics for Business?

For two mutually exclusive events A and B, compute P(A∪B)P\left(A\cup B\right)P(A∪B) if P(A)=0.15P\left(A\right)=0.15P(A)=0.15 and P(B)=0.32P\left(B\right)=0.32P(B)=0.32

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Addition Rule practice set

For two mutually exclusive events A and B, compute $P\left(A\cup B\right)$ if $P\left(A\right)=0.15$ and $P\left(B\right)=0.32$