Probability 3 Question 9

9. An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, then the number of outcomes that B must have, so that A and B are independent, is

(a) 2,4 or 8

(b) 3,6 or 9

(c) 4 or 8

(d) 5 or 10

(2008,3 M)

Show Answer

Solution:

  1. Since, P(A)=25

For independent events,

P(AB)=P(A)P(B)P(AB)25P(AB)=110,210,310,410

[maximum 4 outcomes may be in AB ]

(i) Now, P(AB)=110

P(A)P(B)=110P(B)=110×52=14, not possible 

(ii) Now, P(AB)=21025×P(B)=210

P(B)=510, outcomes of B=5

(iii) Now, P(AB)=310

P(A)P(B)=31025×P(B)=310P(B)=34, not possible 

(iv) Now,

P(AB)=410P(A)p(B)=410

P(B)=1, outcomes of B=10



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