Please show step by step work, thanks! 2. A box in a supply room contains four 4
ID: 3073354 • Letter: P
Question
Please show step by step work, thanks!
2. A box in a supply room contains four 40-Watt light-bulbs, five 60-Watt bulbs, and six 75-Watt bulbs. Suppose that three bulbs are randomly selected. a) b) c) d) What is the probability that it is necessary to examine at least six bulbs? What is the probability that exactly two of the selected bulbs are rated 75 W? What is the probability that all three of the selected bulbs have the same rating? What is the probability that one bulb of each type is selected? Suppose now that bulbs are to be selected one by one until a 75-W bulb is found.Explanation / Answer
Ans
Total number of ways to select 3 light bulbs from 4 40-watt, 5 60-watt and 6 75-watt bulbs
= (4+5+6)!/4!*5!*6!
= 15!/4!*5!*6!
= 630630
a)
Exactly 2 are rated 75-watt
Total number of ways to select 2 bulbs of 75-watt and 1 of any 40-watt or 60-watt= 6C2*9C1 = 15*9 = 135
Total probability = Total number of ways to select 2 bulbs of 75-watt/Total number of ways to select 3 light bulbs of any wattage
=135/630630 = 0.0002
b)
Total ways to select all 3 with the same rating = 3 of 40-watt OR 3 of 60-watt OR 3 of 75-watt
= 4C3*5C3*6C3 = 4*10*20 = 800
Probablity = 800/630630 = 0.0013
c)
Total ways to select one of each type = 4C1*5C1*6C1 = 4*5*6 = 120
Probablity = 120/630630 = 0.0002
d)
Atleast 6 light bulbs to be examined means the first 5 light bulbs are not 75-watt and the sixth is
So,
9C5*6C1 = 126*6 =756/630630 = 0.0012