A box in a supply room contains 21 compact fluorescent lightbulbs, of which 8 ar
ID: 3051716 • Letter: A
Question
A box in a supply room contains 21 compact fluorescent lightbulbs, of which 8 are rated 13-watt, 9 are rated 18-watt, and 4 are rated 23-watt. Suppose that three of these bulbs are randomly selected. (Round your answers to three decimal places.)
(a) What is the probability that exactly two of the selected bulbs are rated 23-watt?
(b) What is the probability that all three of the bulbs have the same rating?
(c) What is the probability that one bulb of each type is selected?
(d) If bulbs are selected one by one until a 23-watt bulb is obtained, what is the probability that it is necessary to examine at least 6 bulbs?
Explanation / Answer
3 bulbs from 21 bulbs can be selected in 21C3 ways
a)
2 bulbs from 4 23-watt bulbs can be selected in 4C2 ways
and remeinining 1 from 17 can be selected in 17C1 wyas
Required probability = 4C2*17/21C3 = 0.0767
b)
P(all are 13-watt) = 8C3/21C3
P(all are 18=watt) = 9C3/21C3
P(all are 23-watt) = 4C3/21C3
Required prob = (8C3 + 9C3 + 4C3)/21C3 = 0.1083
c)
Required prob = (8C1 * 9C1 * 4C1)/21C3 = 0.2165
d)
First 5 bulbs selected are not 23-watt, hence probability = 17C5/21C5 = 0.3041
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.