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Binomial Distribution — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsBinomial Distribution2 Marks
Question
Ten eggs are drawn successively with replacement from a lot containing $10 \%$ defective eggs. Find the probability that there is at least one defective egg.
✓

Answer

Let $X$ denote the number of defective eggs in the 10 eggs drawn.
Since the drawing is done with replacement, the trials are Bernoulli trials.
$
\begin{aligned}
& \text { Probability of success }=\frac{1}{10} \\
& \qquad \begin{aligned}
& p=\frac{1}{10}, q=1-p=1-\frac{1}{10} \quad \therefore \quad q=\frac{9}{10} \\
& X \sim B\left(10, \frac{1}{10}\right) \\
& \quad n=10 \\
& \operatorname{Here} X \geq 1 \\
& P(X \geq 1)=1-{ }^{10} C_0\left(\frac{1}{10}\right)^0 \times\left(\frac{9}{10}\right)^{10} \\
&=1-1 \times 1 \times\left(\frac{9}{10}\right)^{10} \times\left(\frac{9}{10}\right)^{10-x} \\
&=1-\left(\frac{9}{10}\right)^{10}
\end{aligned}
\end{aligned}
$

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