Find and explain some probabilities. Can we have an event A that has negative pr

Question

Find and explain some probabilities. Can we have an event A that has negative probability? Explain your answer. Suppose P(A) = 0.2 and P(B) = 0.4. Explain what it means for A and B to be disjoint. Assuming that they are disjoint, find the probability that A or B occurs. Explain in your own words the meaning of the rule P(S)= 1. Consider an event A. What is the name for the event that A does not occur? If P(A) = 0.3, what is the probability that A does not occur? Suppose that A and B are independent and that P(A) = 0.2 and P(B) = 0.5. Explain the meaning of the event {A and B}, and find its probability.

Explanation / Answer

a)

NO. All probabilitites are at least 0 and at most 1.

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b)

If they are disjoint, by definition,

P(A and B) = 0.

Hence, if A and B are disjoint,

P(A or B) = P(A) + P(B) - P(A and B)

As P(A and B) = 0,

P(A or B) = P(A) + P(B) [ANSWER]

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c)

The probability of a sure event is 1. Here, the sample space makes up all possibilities, so it has probability of 1.

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d)

A' is the event that A does not occur.

Hence, P(A') = 1 - P(A) = 0.7.

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e)

P(A and B) means the probability that both A and B happen.

For independent events,

P(A and B) = P(A)P(B) = 0.1 [ANSWER]

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