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  • Please Solve R .D. Sharma class 12 Chapter 30 Probaility Exercise 30 .4 Question 1 Sub Question 1 Maths Textbook Solution.

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

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Answer: A and B are independent events

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

            A= the first throw results in head, B= the last throw results in tail

Hint: Check, P\left ( A\: \cap\: B \right )=P\left ( A \right )P\left ( B \right )

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

        Thus, A and B are independent events.

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