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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 30 Probaility Exercise 30.5 Question 15 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 30 Probaility  Exercise 30.5 Question 15 Maths Textbook Solution.

Answers (1)

Answer:\frac{23}{364}

Hint: You must know the rules of finding probability.

Given: Bag contains 7 white, 5 black, 4 red balls

Four balls are drawn without replacement.

Solution

We have

White=7, Black=5, Red=4

Four balls are drawn without replacement

P(at least 3 black balls are black)

=P(3 black balls and one not black or 4 black balls)

=P(3 black and one not black)+P(4 black balls)

\begin{aligned} &n C_{r}=\frac{n !}{r !(n-r) !} \\ &=\frac{5 C_{3} \times 11 C_{1}}{16 C_{4}}+\frac{5 C_{4}}{16 C_{4}} \\ &=\frac{51}{31(5-3)} \times \frac{111}{11(11-1)}+\frac{51}{41(5-4)} \\ \end{aligned}

\begin{aligned} &=\frac{16 !}{4 !(16-4) !} \\\\ &=\frac{5 !}{3 ! 2 !} \times \frac{11 !}{10 !}+\frac{5 !}{4 ! 1 !} \\\\ &=\frac{16 !}{4 ! 2 !} \\\\ &=\frac{\frac{5.4}{2} \times 11+5}{\frac{16.15 .14 .13}{4.3 .2}} \end{aligned}

=\frac{\left ( 110+5 \right )}{1820}

=\frac{115}{1820}

=\frac{23}{364}

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