A box in a certain supply room contains four 40-W light-bulbs, five 60-W bulbs,
ID: 3205531 • Letter: A
Question
A box in a certain supply room contains four 40-W light-bulbs, five 60-W bulbs, and six 75- W bulbs. Suppose that three bulbs are randomly selected.
a. What is the probability that exactly two of the selected bulbs are rated 75-W?
b. What is the probability that all three of the selected bulbs have the same rating?
c. What is the probability that one bulb of each type is selected?
d. Suppose now that bulbs are to be selected one by one until a 75-W bulb is found. What is the probability that it is necessary to examine at least six bulbs?
Explanation / Answer
Answer:
A box in a certain supply room contains four 40-W light-bulbs, five 60-W bulbs, and six 75- W bulbs. Suppose that three bulbs are randomly selected.
a. What is the probability that exactly two of the selected bulbs are rated 75-W?
4....40-watt light bulbs
5....60-watt light bulbs
6... 75-watt light bulbs
15 total items in box
C(6, 2) * C(9,1) / C(15,3)
=15*9/455 =0.29670
[2 of the six 75-watt bulbs, 1 of the remaining 9 bulbs]
b. What is the probability that all three of the selected bulbs have the same rating?
[C(4,3)+ C(5,3) + C(6,3)]/C(15,3).
=(4+10+20)/455
=0.0747
c. What is the probability that one bulb of each type is selected?
C(4,1) * C(5,1) * C(6,1) / C(15,3)
=(4*5*6)/455
=0.2637
d. Suppose now that bulbs are to be selected one by one until a 75-W bulb is found. What is the probability that it is necessary to examine at least six bulbs?
1 - Prob (examine at most 5 bulbs)
= 1 - [C(9, 0) * C(6,1) / C(15,1)
+ C(9, 1) * C(6,1) / C(15,2)
+ C(9, 2) * C(6,1) / C(15,3)
+ C(9, 3) * C(6,1)/ / C(15,4)
+ C(9, 4) * C(6,1)] / C(15,5)]
=1-(0.4 + 0.2571 + 0.1582 + 0.0923 + 0.0503)
= 1-0.9579.
=0.0421
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