Question

A box in a supply room contains 15 compat fluorscent lightbulbs, of wich 5 are rated 13 watt, 6 are rated 18 watt, and 4 are rated 23 watt. Suppose that three bulbs are randomly slected.

a- What is the probablity that exactly two of the slected bullbs are rated 23 watt?

b- What is the probablity that all of the three slected bulbs have the same rating?

c- What is the probablity that one of each type is slected ?

Answer 1

The probability of selecting 13W bulb, 18W bulb and 23W bulb is given as follows

(a). There are six cases in which we get exactly two of the selected bulbs as 23W.

Total probability for exactly two as 23W is

(b).

(c).

We have multiplied by 6 because there are six cases in which one of each type of the bulb can be selected in any order. For example, 1st bulb can be of 13W, 2nd of 18W and third of 23W. Another case can be when 1st bulb of 23W, second bulb of 18W and third bulb of 13W and so on.