AP EAMCET · Maths · Probability
If the mean and variance of a binomial variable \(X\) are 2 and 1 respectively, then \(P(X \geq 1)\) is equal to
- A \(\frac{2}{3}\)
- B \(\frac{15}{16}\)
- C \(\frac{7}{8}\)
- D \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{15}{16}\)
Step-by-step Solution
Detailed explanation
Mean \(\Rightarrow n p=2\) and variance \(\Rightarrow n p q=1\) then \(q=\frac{1}{2}, p=\frac{1}{2}\) and \(n=4 \quad(\because p=1-q)\) \(\therefore\) Required probability \(=P(X \geq 1)=1-P(X < 1)\) \(=1-\left(\frac{1}{16}\right)\) \(=\frac{15}{16}\)
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