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Question Video: Using Experimental Probability to Determine the Expected Number of Outcomes of an Event Mathematics

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.

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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.

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