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

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

Answers (1)

Answer: A and B are independent events

Given: Prove that in throwing a pair of dice, the occurrence of the number 4 on the first die is independent of the occurrence 5 on the second die.

Hint: Probaility =\frac{No\: of\: outcomes}{Total\: Outcomes}

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 )

Here, Total number of events = 36

            A = The event of 4 on first die

            B = Event of 5 on second die

            \begin{aligned} &P(A)=\frac{6}{36}=\frac{1}{6} \ldots \ldots .\{(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\} \\ &P(B)=\frac{6}{36}=\frac{1}{6} \ldots \ldots \ldots \ldots . .\{(1,5),(2,5),(3,5),(4,5),(5,5),(6,5)\} \\ &P(A \cap B)=\frac{1}{36} \ldots \ldots \ldots \ldots \ldots . .\{(4,5)\} \end{aligned}

             P\left ( A\cap B \right )=P\left ( A \right )P\left ( B \right )

          Hence,A and B are independent events

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