Q8 of 108 Page 271

Three events A, B and C have probabilities , respectively. Given that and , find the values of P (C | B) and P (A'∩ C').

GIVEN THAT




AND,






AND


By De Morgan’s laws:







(A ∪ B)’ = A’∩ B’
( A∩B)’ = A’∪ B’



P (A'∩ C') = P(A Ս C)’


= 1- P (A Ս C)


= 1-[P(A)+ P(C)- P (A Ո C)]






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6

Explain why the experiment of tossing a coin three times is said to have binomial distribution.

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A and B are two events such that and .

Find:


(i) P(A|B) (ii) P(B|A) (iii) P(A’|B) (iv) P(A’|B’)

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Let E1 and E2 be two independent events such that p(E1) = p1 and P(E2) = p2.

Describe in words of the events whose probabilities are


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(ii)(1-P1-2) P2


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(iv)P1+P2-2P1P2

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A discrete random variable X has the probability distribution given as below:


(i) Find the value of k


(ii) Determine the mean of the distribution.