The events X and Y are mutually exclusive. Suppose P(X) _ .05 and P(Y) _ .02. What is
the probability of either X or Y occurring? What is the probability that neither X nor Y will
happen?

If they're mutually exclusive, then that means they can't both happen ; if one happens, then the other doesn't and vice-versa. You have the individual probabilities for both X and Y. So it should now be easy to calculate the either/or probability. And once you have that answer, it's easy to determine the neither/nor probability as that's simply the complementary event to the either/or probability. I'm not going to give you the actual answers but if you want to attempt it I'll be happy to critique your work.

Mutually exclusive means that one cannot happen of the other happens. For example, if you toss a coin, you either have a head or a tail, not both.

1. The probability that either of the events occur = sum of probability.

2. The probability that neither events occur = Take the probability that either of the events occur from 1.

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Originally Posted by Unknown008

Mutually exclusive means that one cannot happen of the other happens. For example, if you toss a coin, you either have a head or a tail, not both.

1. The probability that either of the events occur = sum of probability.

2. The probability that neither events occur = Take the probability that either of the events occur from 1.

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Here you've been told how to do it, so go for it!

P(X or Y) = P(X) + P(Y)
P(X or Y) = .05 + .02 = .07 is the probability of x or y occurring
P(X or Y) = P(X) + P(Y) -1
P(X or Y) = .05 + .02 -1
P(X or Y) = -.93 probability neither x nor y will happen

The first one is correct.

However, the second one is not. You take 0.07 from 1, that is 1-0.07 and not the other way round. Probability is never negative. Probability ranges from 0 to 1 only.

Quote:

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Originally Posted by Unknown008

The first one is correct.

However, the second one is not. You take 0.07 from 1, that is 1-0.07 and not the other way round. Probability is never negative. Probability ranges from 0 to 1 only.

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You got it!

Thanks for your help. Look forward to collaborating with you again

You're most welcomed! :)