Answer to Question #199341 in Statistics and Probability for Bahawal tahir

Question

Four of the light bulbs in a box of ten bulbs are burnt out or otherwise defective. If two bulbs are selected at random without replacement and tested, (i) what is the probability that exactly one defective bulb is found? (ii) What is the probability that exactly two defective bulbs are found?

Answer 1

Solution:-

Here

probability of bulb is defective = 4/10

p = 0.40

probability of bulb is not defective = 6/10

q = 1-p = 0.60

This question is based on Binomial distribution

$P(x=r) =\space ^n c_r (p)^r(q)^{n-r}$

 (i) what is the probability that exactly one defective bulb is found? 

n=2

and r=1

put in the formula

$P(x=1) =\space ^2 c_1 (0.4)^1(0.6)^{2-1}\\ P(x=1) = 0.48$

(ii) What is the probability that exactly two defective bulbs are found?

 n=2

and r=2

put in the formula

$P(x=2) =\space ^2 c_2 (0.4)^2(0.6)^{2-2}\\ P(x=2) = 0.16$