Suppose A and B are mutually excl and B are mutually exclusive events in a sampl

Question

Suppose A and B are mutually excl and B are mutually exclusive events in a sample space S with probabilities P(A) = 0.25 and P(B) = 0.4 respectively. What is the probability that either A or B occurs? 0.00 0.25 0.55 0.65 0.75 1.00 None of the above. Correct answer is: _____ A and B are events in a sample space S. Event A has probability 0.25: event B has probability 0.55, and the intersection of A and B has probability 0.12. What is the probability of the union of A and B? 0.00 0.46 0.68 0.70 0.83 0.98 None of the above. Correct answer is: _____ A and B are independent events in a sample space S. Suppose that A has probability 0.2 and B has probability 0.5. What is the probability that A and B occur? 0.00 0.10 0.20 0.40 0.60 1.00 None of the above. Correct answer is: _____ Suppose A and B are mutually exclusive events in a sample space S with probabilities P(A) = 0.3 and P(B) = 0.5 respectively. What is the probability that both A and B occur? 0.00 0.05 0.20 0.35 0.65 1.00 None of the above. Correct answer is: _____

Explanation / Answer

When two events (call them "A" and "B") are Mutually Exclusive it is impossible for them to happen together:

P(A and B) = 0

"The probability of A and B together equals 0 (impossible)"

Independent events are events where knowledge of the probability of one doesn't change the probability of the other.

P(A and B) = P(A)*P(B)

1. Here P(A)=0.25 and P(B)=0.45, as events are mutually exclusive P(A and B)=0

As we know P(A or B)=P(A)+P(B)-P(A and B)

So P(A or B)=0.25+0.4=0.65 So D is correct answer

2. Here P(A)=0.25, P(B)=0.55 and P(A and B)=0.12

So P(A or B)=P(A)+P(B)-P(A and B)=0.25+0.55-0.12=0.68 so C is correct answer

3. Here A and B are independent

So P(A and B)=P(A)*P(B)=0.2*0.5=0.10 B is correct answer

4. Here A and B are mutually exclusive events

So P(A and B)=0 so A is correct answer

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