Probability
Expected value of defective pens
nta_pyq_2025_apr
Grade 12
Question:
A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is
$11 15$
$28 75$
$2 15$
$3 5$
Step-by-Step Solution
Key Concept: Use the standard setup for expected value of defective pens and simplify the resulting algebraic condition.
(2) x$x = 0$$x = 1$$x = 2$7 7 3$C_{2}$C$C_{1}$1 3 10 P(x)$C_{2}$10 10$C_{2}$$C_{2}$7 2 3 $\mu$ = $\Sigma$xi P (xi$) = 0$+ + = 15 15 5 2 28 Variance (x) = $\Sigma$Pi (xi - $\mu$$) = 75$
Correct Answer: 2