In a large light bulb factory they manufacture 60 watt 75 wa

In a large light bulb factory, they manufacture 60 watt, 75 watt and 100 watt bulbs. A group of 21 bulbs is selected from this factory for testing. Of the 21 bulbs, 8 are 60 watt, 7 are 75 watt and 6 are 100 watt. A random sample of 3 bulbs is taken from the 21.
a.Find the probability that one bulb of each type (wattage) is selected.
b.Find the probability at least 1 selected bulb is 60 watt.
c.Find the probability that all 3 selected bulbs are the same type (wattage).

Solution

a)

There are 21C3 = 1330 ways to choose 3 bulbs.

There are 8*7*6 = 336 ways to choose so that one of each bulb is selected.

Thus,

P(one of each type) = 336/1330 = 0.252631579 [answer]

*******

b)

P(at least one 60 watt) = 1 - P(no 60 watt)

There are 13C3 = 286 ways to choose 3 non-60 watt bulbs.

Thus,

P(at least one 60 watt) = 1 - P(no 60 watt) = 1 - 286/1330 = 0.784962406 [answer]

********

c)

P(all same type) = P(all 60 or all 75 or all 100)

As there are 8C3, 7C3, and 6C3 ways to choose 3 of each kind of bulbs, then

P(all same type) = (8C3+7C3+6C3)/1330 = 111/1330 = 0.083458647 [answer]