A box in a supply room contains 22 compact fluorescent lightbulbs, of which 8 ar

Question

A box in a supply room contains 22 compact fluorescent lightbulbs, of which 8 are rated 13-watt, 9 are rated 18-watt, and 5 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

Solution

(a) P(2 bulbs are rated 23 watt) = (5C2*17C1)/22C3

= 17/154= 0.1104

(b) P(all 3 have same rating) = (8C3 + 9C3 + 5C3 )/22C3 = 15/154= 0.0974

(c) P(one bulb of each type) = (8C1*9C1*5C1)/22C3 = 18/77 = 0.2338

(d) 1 - Prob (examine at most 5 bulbs)
Do this in cases (1 bulb needed, 2 bulbs needed, ... 5 bulbs needed):

Pr(1 bulb) = 5/22

Pr(2 bulbs) = (17/22)(5/21)

Pr(3 bulbs) = (17/22)(16/21)(5/20)

Pr(4 bulbs) = (17/22)(16/21)(15/20)(5/19)

Pr(5 bulbs) = (17/22)(16/21)(15/20)(14/19)(5/18)

= 1- 0.7650 = 0.2350

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