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  • Explain Solution R.D. Sharma Class 12 Chapter 30 Probability Exercise 30.4 Question 25 Sub Question 2 Maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter 30 Probability  Exercise 30.4 Question 25 Sub Question 2 Maths Textbook Solution.

Answers (1)

Answer: \left ( 1-P_{1} \right )P_{2}=P(A does not occur ,but B Occurs)

Given: Let A and B be two independent events such that

             P\left ( A \right )=p_{1}\&P\left ( B \right )=p_{2}

Hint: Use  P\left ( A \right )+P\left ( \bar{A} \right )=1

Solution: As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e. P\left ( A\cap B \right )=P\left ( A \right )P\left ( B \right )

                        \begin{aligned} &\left(1-P_{1}\right) P_{2}=[1-P(A)] \times P(B) \\ \end{aligned}

                                               \begin{aligned} &=P(\bar{A}) \times P(B) \\ \end{aligned}

And A and B are independent events

                           \begin{aligned} &\text { ie, } \mathrm{P}(\overline{\mathrm{A}}) \times \mathrm{P}(\mathrm{B})=\mathrm{P}(\overline{\mathrm{A}} \cap \mathrm{B}) \\ &\text { So, } \mathrm{P}(\overline{\mathrm{A}} \cap \mathrm{B})=\left(1-\mathrm{P}_{1}\right) \mathrm{P}_{2} \end{aligned}

Hence,\left ( 1-P_{1} \right )P_{2}=P(A does not occur ,but B Occurs)

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