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  • Need solution for RD sharma maths class 12 chapter 30 probablity exercise Very short answer question, question 17

Need solution for RD sharma maths class 12 chapter 30 probablity exercise Very short answer question, question 17

Answers (1)

The required expression is P(A)+P(B)-2P(A).P(B)

Hint:

If A and B are independent then P(A\cap B)=P(A).P(B)  and

P(exactly one of the two events occurs) = P(A \cup B)-P(A \cap B)

Given:

A and B are independent events

Explanation:

It is given that ,

A and B are independent events

Now ,

P(exactly one of the two events occurs) = P(A \cup B)-P(A \cap B)

=P(A)+P(B)-P(A\cap B)-P(A\cap B)

=P(A)+P(B)-P(A).P(B)-P(A).P(B)              (\therefore A , B are independent)

=P(A)+P(B)-2P(A).P(B)

Hence, the required expression is P(A)+P(B)-2P(A).P(B)

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