Suppose each light bulb you test, from a batch of newly produced light bulbs, is
ID: 3254761 • Letter: S
Question
Suppose each light bulb you test, from a batch of newly produced light bulbs, is good with probability 93%, independently of any other light bulbs. (a) If you choose 6 light bulbs, what is the probability they are all good? (b) If you choose 6 light bulbs, what is the probability they are all bad? (c) What is the probability that out of 6 light bulbs, exactly 1 is bad? (d) What is the probability that out of 6 light bulbs, at least 1 is bad? (e) What is the probability that out of 6 light bulbs, at least 2 are bad?Explanation / Answer
P(good bulb) = 0.93
p(bad bulb) = 0.07
a)
Probability that all 6 good bulb is 0.936 = 0.64699
b)
Probability that all 6 bad bulb is 0.076
c)
Probability that exactly 1 is bad in 6 light bulb is
6C1 0.071 0.935 = 0.2922
d)
Probability that in 6 light bulb at least 1 is bad = 1 - probability that all bulbs good.
= 1 - 0.6499
= 0.35301
e) Probability that at least 2 bad out of 6 bulbs is
6C2 0.072 0.934 + 6C3 0.073 0.933 + 6C4 0.074 0.932 +6C5 0.075 0.93 + 6C6 0.076
= 0.06082