Question

80 bulbs are selected at random from a lot and their times (in hours) is recorded in the form of a frequency table given below :

Lifetime (in hours)	300	500	700	900	1100
Frequency	10	12	23	25	10

One bulb is selected at random from the lot. Then find the probability that its life is 1150 h.

Answer 1

Hint: Probability of an event A, is the ratio of the number of outcomes favourable to the event, to the total number of outcomes. Event is the occurrence/ experiment whose probability has to be found.
P(A) = $\dfrac{{{\rm{\text{number of favourable outcomes}}}}}{{{\rm{\text{total number of outcomes}}}}}$.

Complete step by step solution:
Step 1
Given table:

Lifetime (in hours)	300	500	700	900	1100
Frequency	10	12	23	25	10

Step 2
Number of bulbs with lifetime of 1150 h = 0

Step 3
Total number of bulbs in the lot = 80

Step 4
Probability (one bulb with life time of 1150 h) $ = \dfrac{{{\rm{\text{number of favourable outcomes}}}}}{{{\rm{\text{total number of outcomes}}}}}$
                                                                                    $ = \dfrac{0}{{80}}$
                                                                                     = 0

Therefore, Probability of one bulb selected at random with lifetime 1150 h is 0.

Note:
Probability of any event is always “greater than and equal to 0” and “less than and equal to 1”.
The set of all possible outcomes is called the sample space, S of the experiment. Any subset E of sample space S is called an event. The probability of event, E is given by:
P(E) = $\dfrac{{n(E)}}{{n(S)}}$
Where, $n(E)$ is the number of elements in set E, $n(S)$ is the number of elements in the set S.