# Video: Determining the Experimental Probability of an Event

A game at a festival challenged people to throw a baseball through a tire. Of the first 68 participants, 3 people won the gold prize, 12 won the silver prize, and 15 won the bronze prize. What is the experimental probability of not winning any of the three prizes?

02:50

### Video Transcript

A game at a festival challenged people to throw a baseball through a tire. Of the first 68 participants, three people won the gold prize, 12 won the silver prize, and 15 won the bronze prize. What is the experimental probability of not winning any of the three prizes?

Let’s begin this by picking out the key pieces of information. Three people won the gold prize, 12 people won the silver prize, and 15 people won the bronze prize. However, we’re told that 68 people tried the game. And if we add together the three, the 12 and the 15 people that won prizes, this will add up to 30, which means that there must be 38 people who didn’t win any prize since 68 subtract 30 gives us 38.

The question, however, is not simply asking how many people didn’t win a prize, but instead it’s asking for the experimental probability. We can recall that to calculate the experimental probability of an event E. This is equal to the number of times E occurs divided by the total number of trials. We can answer this question using two different possible methods, but each one will still use the same formula.

In the first method, we can write that the probability of not winning a prize is equal to the number of non-prize winners divided by the number of participants. And therefore, as we have 38 people who didn’t win a prize divided by 68 people in total, this would be the fraction 38 over 68. We can then further simplify this faction to give 19 over 34. Let’s record this value up here so that when we clear the screen and try the second method, we can check that both would give the same result.

For the second method, we’re going to use the total probability rule, which tells us that the sum of all probabilities is equal to one. In the method we’ve just seen, we worked out the probability of not winning a prize. In the second method, we’re going to calculate the probability of winning a prize and then subtract it from one. So, in our second method, we’re going to calculate the probability of winning a prize, which is equal to the number of prize winners divided by the number of participants.

Adding together all the prize winners give us 30. And since we still have 68 people, then this will be 30 over 68. We can then simplify this to give us the fraction 15 over 34. And now, using our total probability rule, we would have the probability of not winning a prize is equal to one subtract 15 over 34 which is 19 over 34 since we could write one as the fraction 34 over 34. And, therefore, using either method would give us that the experimental probability of not winning any of the prizes is 19 over 34.