A box in a certain supply room contains four 40-W lightbulbs, five 60-W bulbs, and six 75-W
bulbs.
i. Suppose that three bulbs are randomly selected. What is the probability that exactly
two of the selected bulbs are rated 75 W?
ii. If two bulbs are randomly selected from the box of lightbulbs and at least one of them
is found to be rated 75 W, what is the probability that both of them are 75-W bulbs?
iii. Given that at least one of the two selected is not rated 75 W, what is the probability
that both selected bulbs have the same rating?
Answers
Answer:
Step-by-step explanation:
There are (12 C 3) = 220 ways to choose 3 bulbs.
a) Exactly two 75W can happen (5C2) = 10 ways.
One non-75W can happen (7C1) = 7 ways.
Combination can happen 10 * 7 = 170 ways.
Probability = 170/220 = .77 or 77%
b) All three the same can happen 3 ways; 40-40-40, 60-60-60, 75-75-75.
(4C3) + (3C3) + (5C3) = 4 + 1 + 10 = 15 ways
Probability = 15 /220 = .07678 or 7.678%
c) One of each can happen (4C1) * (4C1) * (7C1) = 112 ways
Probability = 112 / 560 = .0681 or 6.81%
d) The only way that at least 6 bulbs are required is if the first 5 are chosen from the 7 non-75W bulbs.
There are (12 C 5) = 792 ways to choose the first 5 bulbs.
Of those (7C5) = 21 ways to choose from only the non-75W bulbs
Probability = 21 / 792 = .0265 or 2.65%