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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.
Solution
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`
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