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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 30 Probability Exercise 30.4 Question 15 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 30 Probability  Exercise 30.4 Question 15 Maths Textbook Solution.

Answers (1)

Answer: \frac{6}{2197}

Hint: Use permutations for finding  { }^{n} P_{r}=\frac{n !}{(n-r) !}

Given:

Three cards are drawn with replacement from a well shuffled pack of cards. Find the probability that the cards drawn are king, queen and jack.

Solution:

Let,

            A= Event of getting kings

             P\left ( A \right )=\frac{No.\: of\: cards\: of\: king}{Total\: no.of\: cards}=\frac{4}{52}

            Similarly, B= Event of getting queens

                           P\left ( B \right )=\frac{No.\: of\: cards\: of\: queens }{Total\: no.of\: cards}=\frac{4}{52}

                        C= Event of getting jacks

                        P\left ( C \right )=\frac{No.\: of\: jack\: cards\: }{Total\: no.of\: cards}=\frac{4}{52}

Probability that cards drawn are king, queen and jack  =\frac{4}{52}\times \frac{4}{52}\times \frac{4}{52}\times 3P_{2}

(Permutations has been used because the order of king,queen and jack can be changed) 

                                                                                   \begin{aligned} &=\frac{4 \times 4 \times 4 \times 6}{52 \times 52 \times 52} \\ &=\frac{6}{2197} \end{aligned}

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