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  • Please Solve R.D.Sharma class 12 Chapter 30 Probaility Exercise 30.4 Question 1 Sub Question 2 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 30 Probaility  Exercise 30.4 Question 1 Sub Question 2 Maths Textbook Solution.

Answers (1)

Answer: A and B are not independent events

Given: A coin is tossed thrice and all the eight outcomes are assumed equally likely.

            A= the number of heads is odd, B= the number of tails is odd

Hint: Check, P\left ( A\cap B \right )=P\left ( A \right )P\left ( B \right ) or not

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 )

Let,

        \begin{aligned} &S=\left\{\begin{array}{l} (\mathrm{HHH}),(\mathrm{HHT}),(\mathrm{HTH}),(\mathrm{HTT}) \\ (\mathrm{THH}),(\mathrm{THT}),(\mathrm{TTH}),(\mathrm{TT}) \end{array}\right\} \\ \end{aligned}

        \begin{aligned} &\mathrm{P}(\mathrm{A})=\frac{4}{8}=\frac{1}{2} \\ &\mathrm{P}(\mathrm{B})=\frac{4}{8}=\frac{1}{2} \\ &\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{0}{8}=0 \\ \end{aligned}

 Here \begin{aligned} &\mathrm{P}(\mathrm{A} \cap \mathrm{B})\neq \mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}) \end{aligned}

Thus, A and B are not independent events.

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