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  • Explain solution for RD Sharma maths class 12 chapter 31 Mean and Variance of a Random Variable exercise multiple choice questions question 2 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 31 Mean and Variance of a Random Variable exercise multiple choice questions question 2 maths textbook solution

Answers (1)

Answer:

              0.77

Hint:

              To solve this we use P\left ( E\cup F \right )=P\left ( E \right )+P\left ( F \right )-P\left ( E\cap F \right )

Given:

              

X 1 2 3 4 5 6 7 8
P\left ( X \right ) 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05

Solution:

\begin{aligned} &P(E \cup F)=P(E)+P(F)-P(E \cap F) \\ &P(E)=P(X=2)+P(X=3)+P(X=5)+P(X=7) \ldots\{\text { prime numbers from } 1 \text { to } 8\} \\ &=0.23+0.12+0.2+0.07 \\ &=0.62 \end{aligned}

\begin{aligned} &P(F)=P(X=1)+P(X=2)+P(X=3) \ldots\{X<4\} \\ &=0.15+0.23+0.12 \\ &=0.50 \\ \end{aligned}

\begin{aligned} &P(E \cap F)=P(\text { Xisaprimenumber }<4) \\ &=P(X=2)+P(X=3) \\ &=0.23+0.12 \\ &=0.35 \\ \end{aligned}

\begin{aligned} &P(E \cap F)=P(E)+P(F)-P(E \cap F) \\ &=0.62+0.50-0.35 \\ &=0.77 \end{aligned}

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