Exams Joint Entrance Examination Mathematics Probability Question 25 Question 25 of 417 Medium MCQ
Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x x x denote the number of defective oranges, then th...
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\[ Probability distribution \[ x i p i x = 0 7 C 2 10 C 2 = 42 90 x = 1 7 C 1 × 3 C 1 10 C 2 = 42 90 x = 2 3 C 2 10 C 2 = 6 90 \begin{aligned}
&\text { Probability distribution }\\
&\[\begin{array}{|ccccc|}\mathrm{x}_{\mathrm{i}} & \mathrm{p}_{\mathrm{i}} \\ \\ \mathrm{x}=0 & \frac{{ }^7 \mathrm{C}_2}{{ }^{10} \mathrm{C}_2}=\frac{42}{90} \\ \\ \mathrm{x}=1 & \frac{{ }^7 \mathrm{C}_1 \times{ }^3 \mathrm{C}_1}{{ }^{10} \mathrm{C}_2}=\frac{42}{90} \\ \\ \mathrm{x}=2 & \frac{{ }^3 \mathrm{C}_2}{{ }^{10} \mathrm{C}_2}=\frac{6}{90}\end{array}\end{aligned} Probability distribution \[ x i x = 0 x = 1 x = 2 p i 10 C 2 7 C 2 = 90 42 10 C 2 7 C 1 × 3 C 1 = 90 42 10 C 2 3 C 2 = 90 6 \]
\]
\[ \begin{aligned}
&\text { Now, }\\
&\begin{aligned}
& \mu=\sum \mathrm{x}_{\mathrm{i}} \mathrm{p}_{\mathrm{i}}=\frac{42}{90}+\frac{12}{90}=\frac{54}{90} \\
& \sigma^2=\sum \mathrm{p}_{\mathrm{i}} \mathrm{x}_1^2-\mu^2=\frac{42}{90}+\frac{24}{90}-\left(\frac{54}{90}\right)^2 \\
& \Rightarrow \frac{66}{90}-\left(\frac{54}{90}\right)^2 \\
& \sigma^2 \Rightarrow \frac{28}{75} \therefore(1)
\end{aligned}
\end{aligned}\] Answer the question to unlock