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9. O0/4 points | Previous Answers A box in a certain supply room contains seven

ID: 3070103 • Letter: 9

Question

9. O0/4 points | Previous Answers A box in a certain supply room contains seven 40-W lightbulbs, five 60-W bulbs, and four 75-W bulbs. Suppose that three bulbs are randomly selected. (Round your answers to four decimal places.) (a) What is the probability that exactly two of the selected bulbs are rated 75-W? 0.2182 (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? Need Help? ReadtTaik to a Tutor

Explanation / Answer

3 bulbs from 16 can be selected in 16C3 ways

a)
two bulbs of 75-W can be selected in 4C2 ways and 1 from remiaining 12 can be selected in 12C1

Probability = 4C2*12C1/16C3 = 0.1286

b)
3 from 7 40W can be selected in 7C3
OR 3 from 5 60W can be selected in 5C3
OR 3 from 4 75W can be selected in 4C3

Required probability = (7C3 + 5C3 + 4C3)/16C3
= 0.0875

c)
1 from 7 40W can be selected in 7C1
AND 1 from 5 60W can be selected in 5C1
AND 1 from 4 75W can be selected in 4C1

Required probability = (7C1 * 5C1 * 4C1)/16C3
= 0.25

d)
Probability that no 75W bulb selected in first 5 selections is 12C5/16C5 = 0.1813

Required probability = 1 - 0.1813 = 0.8187