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  • Need solution for RD Sharma Maths Class12 Chapter 30 Probability Exercise Fill in the Blanks Question, Question 17.

Need solution for RD Sharma Maths Class12 Chapter 30 Probability Exercise Fill in the Blanks Question, Question 17.

Answers (1)

Answer:   0

Given:

If A and B are two events
then, P (exactly one of A and B occurs )=…

Hint:

P(A or B)=P(A)+P(B)-2P(A\cap B)

Explanation:

\begin{aligned} &P(A \cup B)=P(A \cap B) \\ &\Rightarrow P(A)+P(B)-P(A \cap B)=P(A \cap B) \\ &\Rightarrow P(A)+P(B)-2 P(A \cap B)=0 \end{aligned}

Also P( exactly one of  A and B occurs) = P( A or B)

\begin{aligned} \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B}) &=2(\mathrm{P}(\mathrm{A} \cap \mathrm{B})) \\ &=0 \end{aligned}                                                                      [\because of (1)]

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