Assume that p(a) = 0.4 and p(b) = 0.7. making no further assumptions on a and b, show that p(ab) satisfies 0.1 ⤠p(ab) ⤠0.4.

Step-by-step explanation:

Given that P(A) = 0.4 and P(B) = 0.7.

No further information is known about A or B

But we can say that from addition theorem of probability that

The greatest value P(AB) can take will be

since P(A) is less than P(B)

If one is a subset of Other, only A can be a subset of B.

If one set is a subset of other then we have maximum probability for their intersection.

Here P(AB) cannot exceed 0.4 the probability of smaller set A

Put together

P(AB) lies between 0.1 and 0.4

is there a picture

step-by-step explanation:

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