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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