Number of defective bulbs in a lot of 500 bulbs follows a binomial distribution with probability of a randomly selected bulb to be defective equal to 0.3 A. A sample of 50 bulbs is drawn. Probability of 2 defective bulbs in the sample is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $1225 (0.3)^2 (0.7)^{48}$
No. of drawn = 50
S = success = defective bulb drawn
$P(S) = 0.3$
$P(\overline S)=0.7$
$P(S=2)={^{50}C}_2×0.3^2×0.7^{48}$
$=\frac{50×49}{2}×0.3^2×0.7^{48}$
$=1125(0.3)^2(0.7)^{48}$