Question

The following table gives the life time of 400 neon lamps:

Life time (in hours)	300-400	400-500	500-600	600-700	700-800	800-900	900-1000
Number of lamps:	14	56	60	86	74	62	48

A bulb is selected of random, Find the probability that the  the life time of the selected bulb is:
(i) less than 400
(ii) between 300 to 800 hours
(iii) at least 700 hours.

Answer 1

The total number of trials is 400.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by P (A) and is given by

` P(A) = m/n`

(i) Let A₁ be the event that the lifetime of a chosen bulb is less than 400 hours.

The number of times A₁ happens is 14.

Therefore, we have

`P (A_1)=14/400`

            =`7/200`

(ii) Let A₂ be the event that the lifetime of a chosen bulb is in between 300 to 800 hours.

The number of times A₂ happens is 14 +56+60+86+74 =290 .

Therefore, we have

`P (A_2)=290/400`

            =`29/40` .

(iii) Let A₃ be the event that the lifetime of a chosen bulb is atleast 700 hours.

The number of times A₃ happens is 74+62+48=184 .

Therefore, we have

`P (A_3)=184/400`

            =`23/50`