A box in a certain supply room contains seven 40+_w lightbulbs, four 60_W bulbs,
ID: 3274913 • Letter: A
Question
A box in a certain supply room contains seven 40+_w lightbulbs, four 60_W bulbs, and five 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? (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
Number of 40W bulbs = 7
Number of 60-W bulbs = 4
Number of 75-W bulbs = 5
Total number of ways to select three bulbs = 16C3 = 560
(a) The two 75-W bulbs can be selected in 5C2 = 10 ways
The remaining bulb can come in 4+5 = 9 ways
The the three bulbs can come in 10*9 = 90 ways
Probability = 90/560 = 0.1607
(b) Number of ways that the three bulbs are all 40-W = 7C3 = 35
Number of ways that the three bulbs are all 60-W = 4C3 = 4
Number of ways that the three bulbs are all 75-W = 5C3 = 10
=> Number of ways that the three bulbs are rated same = 35 + 4 + 10 = 49
Probability = 49/560 = 0.0875
(c) The three bulbs can be selected in 7*4*5 = 140 ways
Probability = 140/560 = 0.25
(d) The probability that the first bulb is not a 75-W bulb
= (7+4) / 16
= 11 / 16
=> The probability that the first five bulbs are not 75-W bulbs
= (11/16)5
= 0.1536
Thus the probability that it is necessary to examine atleast six bulbs
= 0.1536
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