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 2 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 2 mutually exclusive events, the probability of a or b happening happening is simply equal to the probability of a plus the probability of b. So all we need to do is plug our values in here. Now we know that the probability of a is this is 0.15, and the probability of b is 0.32. So plugging these values in and adding them together, I get the that 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.

4. Probability

Addition Rule

Statistics

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 $P\left(B\right)=0.32$

$0.048$

$0.17$

$0.47$

$0.53$

Verified step by step guidance

Understand that mutually exclusive events A and B cannot occur at the same time, meaning P(A ∩ B) = 0.

Recall the formula for the probability of the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Since A and B are mutually exclusive, substitute P(A ∩ B) = 0 into the formula: P(A ∪ B) = P(A) + P(B).

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

Add the probabilities to find P(A ∪ B).

5:14m

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Struggling with Statistics?

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 $P\left(B\right)=0.32$