Question

The following table gives the life times of 500 CFL lamps.

Lifetime (months)	9	10	11	12	13	14	More than 14
Number of lamps	26	71	82	102	89	77	53

A bulb is selected at random. Find the probability that the lifetime of the selected bulbs are more than 14 months.
a. \[\dfrac{{53}}{{500}}\]
b. \[\dfrac{{52}}{{500}}\]
c. \[\dfrac{3}{{500}}\]
d. none of these

Answer 1

Hint:\[Probability{\text{ }}of{\text{ }}event{\text{ }}to{\text{ }}happen{\text{ }}P\left( E \right){\text{ }} = {\text{ }}\dfrac{{Number{\text{ }}of{\text{ }}favorable{\text{ }}outcomes}}{{total{\text{ }}Number{\text{ }}of{\text{ }}outcomes}}\]

Complete step-by-step answer:
The number of favorable outcomes for 9 months is 26.
The number of favorable outcomes for 10 months is 71.
The number of favorable outcomes for 11 months is 82.
The number of favorable outcomes for 12 months is 102.
The number of favorable outcomes for 113 months is 89.
The number of favorable outcomes for 14 months is 77.
The number of favorable outcomes more than 14 is 53.
Total number of outcomes is the sum of the favorable outcomes for the 9,10,11,12,13,14,more than 14 months.
\[ \Rightarrow \]Total number of outcomes = 26+71+82+102+89+77+53=500
 Probability that the lifetime of the selected bulb is more than 14 months is: \[{\text{Probability of number of moths more than 14}} = {\text{ }}\dfrac{{{\text{Number of lamps of the months more than14}}}}{{{\text{total Number of outcomes}}}}\]
\[ = \dfrac{{53}}{{500}}\]
Therefore, probability that the lifetime of the selected bulb is more than 14 months is \[\dfrac{{53}}{{500}}\]
i.e, option A.


Note: We can also do the sum in following method:
Probability of the life times more than 14 months=1- Probability of the life times less than or equals to 14 months
\[ = 1 - \dfrac{{447}}{{500}}\]= \[\dfrac{{53}}{{500}}\]
Therefore, the probability that the lifetime of the selected bulb is more than 14 months is \[\dfrac{{53}}{{500}}\] .