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An experiment has 10 equally likely outcomes.Let A and B be 2 non-empty events of the experiment.If A consists of 4 outcomes,the no. of outcomes that B must have so that A and B are independent is ? Ans given is " 5 or 10 ". Please explain.

An experiment has 10 equally likely outcomes.Let A and B be 2 non-empty events of the experiment.If A consists of 4 outcomes,the no. of outcomes that B must have so that A and B are independent is ?

Ans given is
" 5 or 10 ".
Please explain.

Grade:12

1 Answers

Sudheesh Singanamalla
114 Points
11 years ago

As a and b are independent events.

P(A intersection B) = P(A).P(B)

N of (A intersection B) / 10 = N(A) .N(B) / 100 = 4 * N(B) /100

 

5 * N(A intersection B) = 2N(B)

5 | 2 N(B) ==> 5 | N(B)  doesnot divide 2

 

therefore N(B) = 5 or 10

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