MHT CET · Maths · Statistics
A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one by one, with replacement, then the variance of the number of green balls drawn is
- A 6
- B 4
- C \(\frac{6}{25}\)
- D \(\frac{12}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{12}{5}\)
Step-by-step Solution
Detailed explanation
Probability of green ball \((p)=\frac{15}{25}=\frac{3}{5}\)
Probability of yellow ball \((q)=\frac{10}{25}=\frac{2}{5}\)
Also, \(\mathrm{n}=10\)
\(\begin{aligned}
\therefore \quad \text { Variance } & =\mathrm{npq} \\
& =10\left(\frac{3}{5}\right)\left(\frac{2}{5}\right)=\frac{12}{5}
\end{aligned}\)
Probability of yellow ball \((q)=\frac{10}{25}=\frac{2}{5}\)
Also, \(\mathrm{n}=10\)
\(\begin{aligned}
\therefore \quad \text { Variance } & =\mathrm{npq} \\
& =10\left(\frac{3}{5}\right)\left(\frac{2}{5}\right)=\frac{12}{5}
\end{aligned}\)
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