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  • Explain Solution R.D. Sharma Class 12 Chapter 31Mean and Variance of a Random Variable Exercise 31.2 Question 17 maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter 31Mean and Variance of a Random Variable  Exercise 31.2 Question 17 maths Textbook Solution.

Answers (1)

Answer:

1.5

Hint:

MeanE\left ( X \right )=\sum_{i-1}^{n}X_{i}P_{i}

Given:

Three cards are drawn at randomly from a shuffle pack of 52 cards  

Solution:

In 52 cards

26 = Red

26 = Black

Number of outcomes

3 Red 0 Black

2 Red 1 Black

1 Red 2 Black

0 Red 3 Black

\begin{aligned} &P(X=0)+P(X=1)+P(X=2)+P(X=3) \\\\ &=\frac{26 C_{0} \times 26 C_{3}}{52 C_{3}}+\frac{26 C_{1} \times 26 C_{2}}{52 C_{3}}+\frac{26 C_{2} \times 26 C_{1}}{52 C_{3}}+\frac{26 C_{3} \times 26 C_{0}}{52 C_{3}} \\\\ &=1.5 \\\\ &\text { Mean } E(X)=\sum_{i=1}^{n} x_{i} p_{i}=\frac{3}{2}=1.5 \end{aligned}

 

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