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Question

Mean and variance of binomial variable X are 2 and 1 respectively, then $$ \displaystyle P\left ( X\geq 1 \right ) $$ is


A
23
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B
78
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C
45
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D
1516
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Solution

The correct option is D $$ \displaystyle \frac{15}{16} $$
Here,  $$np = 2,  npq =1$$
$$\therefore p=q=\cfrac{1}{2}, n =4$$
$$\therefore P(X\geq 1) =1-P(X =0)=1-^4C_0 \left(\cfrac{1}{2}\right)^4 =1-\cfrac{1}{16}=\cfrac{15}{16}$$

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