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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 30 Probaility Exercise 30.4 Question 5 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 30 Probaility  Exercise 30.4 Question 5 Maths Textbook Solution.

Answers (1)

Answer: A and B are independent events

Hint: Use formula P\left ( A\cap B \right )=P\left ( A \right )+P\left ( B \right )-P\left ( A\cap B \right )

 

Given:

            P\left ( A \right )=\frac{1}{4}

            P\left ( B \right )=\frac{1}{3}

            P\left ( A\cap B \right )=\frac{1}{2}

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 )

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

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

                      =\frac{1}{4}+\frac{1}{3}-\frac{1}{2}

                       =\frac{3+4-6}{12}

P\left ( A\cap B \right )=\frac{1}{12}=\frac{1}{4}\times P\left ( A \right )P\left ( B \right )

Thus, A and B are independent events.

 

 

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