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  • Please Solve R.D.Sharma class 12 Chapter 30 Probaility Exercise 30.4 Question 3 Sub Question 2 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 30 Probaility  Exercise 30.4 Question 3 Sub Question 2 Maths Textbook Solution.

Answers (1)

Answer: A and B are independent events

Given: A card is drawn from a pack of 52 cards so that each card is equally likely to be selected.

            A= the card is black, B= the card drawn is a king

Hint: To find events are independent 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, A =Event of getting a black card

            P\left ( A \right )=\frac{Number\: of\: Black\: Cards}{Total\: Number\: of\: Cards}

                          =\frac{26}{52}.....(Total \: Number\: of\: black\: cards=26)

                            =\frac{1}{2}

        B = Event of getting an king

        P\left ( B \right )=\frac{Number\: of\: Black\: Cards}{Total\: Number\: of\: Cards}

                      =\frac{4}{52}

                       =\frac{1}{13}

          P\left ( A\cap B \right )=\frac{2}{52}.....\left \{ N.\: of\: black\: kings=2 \right \}

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

Thus, A and B are independent events.

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