PROBLEM 3. A box in a certain supply room contains three types of light bulbs: s

Question

PROBLEM 3. A box in a certain supply room contains three types of light bulbs: seven 60-W lightbulbs, five 75-W bulbs, and eight 100-W bulbs. Suppose that three light bulbs are randomly selected. (Round up your answers to 3 decimal places). a. Find the probability that all selected light bulbs are 60-W. Answer: b. Find the probability that exactly two of the selected light bulbs are 100-W Answer: c. Find the probability that one light bulb of each type is selected. Answer: d. Find the probability that all three of the selected light bulbs have the same type. Answer:

Explanation / Answer

a) total number of bulbs = 7 + 5 +8 = 20 bulbs

60 W - 7 ,

75 W - 5

100 W - 8

3 bulbs are selcted

total number of ways of selecting 3 bulbs = 20C3 = 20*19*18/6 = 20*57 = 1140

probability that all bubs selected are 60-W = 7C3 /20C3

= 7 * 6 * 5 /(20*19*18)

= 0.0307017

b)

100 W - 8 , other - 12

Probability of 2 100 W = 8C2 * 12C1 / 20C3

= (8 * 7/2   *12)/1140

=0.2947368

c)

Probability that one light of each type is selected

= 7*8*5/1140

= 0.24561

d)

Probability that all selected bulbs are of same type

= (7C3 + 5C3 + 8C3)/20C3

= (7*6*5 + 5 * 4*3 + 8*7*6)/(20*19*18)

= 0.0885964

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