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.
