A box containing 10 wall clocks has three defective pieces in it. If random sample of two clocks is taken from the box, then the probability distribution of defective clocks is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → X 0 1 2 P(X) \( \displaystyle\frac{7}{15} \) \( \displaystyle\frac{7}{15} \) \( \displaystyle\frac{1}{15} \)
Let X be the number of defective clocks in the sample. The two clocks are taken together (without replacement), so we count selections: there are 7 good and 3 defective clocks, and \( ^{10}C_{2}=45 \) possible samples.
\( \displaystyle P(X=0)=\frac{^{7}C_{2}}{^{10}C_{2}}=\frac{21}{45}=\frac{7}{15} \)
\( \displaystyle P(X=1)=\frac{^{7}C_{1}\cdot{}^{3}C_{1}}{^{10}C_{2}}=\frac{21}{45}=\frac{7}{15} \)
\( \displaystyle P(X=2)=\frac{^{3}C_{2}}{^{10}C_{2}}=\frac{3}{45}=\frac{1}{15} \)
Check: \( \frac{7}{15}+\frac{7}{15}+\frac{1}{15}=1 \).
CBSE Applied Mathematics (Class XII):
Mathematical Expectation of Discrete Probability Distribution
