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  • Please Solve R.D.Sharma class 12 Chapter 30 Probaility Exercise 30.4 Question 4 Sub Question 2 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 30 Probaility  Exercise 30.4 Question 4 Sub Question 2 Maths Textbook Solution.

Answers (1)

Answer: B and C are not independent events

Given: A coin is tossed three times. A = first toss is head, B= second toss is head, C=exactly two heads are tossed in a row. Check the independence of B and C

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

 Thus, B and C are not independent events.

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