### Video Transcript

A light bulb manufacturer examined
a sample of 1000 light bulbs from their production. Using the table which shows the
results for this sample, calculate the experimental probability that a light bulb
fails after less than 150 hours of use.

In this problem, a manufacturer is
testing the life span of a sample of 1000 light bulbs that have been
manufactured. These life spans are entered into a
table, with the first group being light bulbs that last for less than 150 hours and
the second group being greater than or equal to 150 hours but less than 400
hours. The following two groups represent
life spans of 400 or more hours but less than 1000 hours. And the final group is the bulbs
that last 1000 hours or more. In context, a light bulb which has
a longer life span would be considered better for a customer.

Here, we need to find the
experimental probability that a light bulb fails after less than 150 hours of
use. Knowing this would be very useful
in real life, because with something like light bulbs, a manufacturer can’t test
every light bulb they produce because that would destroy each one, and then they
couldn’t sell them. So let’s recall how we calculate
the experimental probability of an event.

In general, we can say that the
experimental probability of an event is equal to the number of trials in which the
outcome occurred over the total number of trials. In the context here, the
experimental probability that a light bulb fails after less than 150 hours is equal
to the number of light bulbs failing after less than 150 hours over the total number
of light bulbs. We then just need to work out the
values for the numerator and denominator on the right-hand side.

Using the table, we can see that
the number of bulbs lasting less than 150 hours is 150. Be careful to note that we are
using the frequency here, that’s the number of lamps, rather than the 150 coming
from the less than hours. Then, we were given that there were
1000 light bulbs tested. Even if we weren’t given this in
the introduction to the problem, we could have calculated this value of 1000 by
adding up the values of 150, 320, 270, and 260 given in the second row of the
table.

So this experimental probability
can be written as a fraction of 150 over 1000. We can then simplify this fraction
to give the answer that the experimental probability that a light bulb fails after
less than 150 hours is three over 20. But a decimal value of 0.15 or a
percentage value of 15 percent would also be valid answers for this probability.