Probability 2 Question 8

8. For two given events A and B,P(AB) is

(1988, 2M)

(a) not less than P(A)+P(B)1

(b) not greater than P(A)+P(B)

(c) equal to P(A)+P(B)P(AB)

(d) equal to P(A)+P(B)+P(AB)

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Answer:

Correct Answer: 8. (a)

Solution:

  1. We know that,

P(AB)=P(A)+P(B)P(AB)

Also, P(AB)1

P(AB)min., when P(AB)max=1P(AB)P(A)+P(B)1

Option (a) is true.

Again, P(AB)0

P(AB)max, when P(AB)min.=0

P(AB)P(A)+P(B)

Option (b) is true.

Also, P(AB)=P(A)+P(B)P(AB), Thus, ( c) is also correct.

Hence, (a), (b), (c) are correct options.



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