This is Stephanie from StatisticsHowTo.com.
And in this video I will go over a few problems that involve the probability of something
not happening. I am going to go over three different question
types. The first type of question you are likely
to encounter is one like this. If the probability a major hurricane will
hit Florida this year is 0.49, then what’s the probability a major hurricane does
not hit Florida this year? We take 100 percent and you subtract the given
probability. This is given as a decimal it is 0.49.
I am going to change that to a percentage, 49 percent that gives me 51 percent.
If you don’t want to deal with percentages instead of a 100 percent.
We could just say 1 and then we can subtract the decimal 0.49 and that will give you 0.51.
That brings me to my second problem type. This time we are given 27 percent of Americans
support Universal Health Care. If an American adult is chosen at random.
What is the probability they will not support Universal Health Care?
Well we have got 27 percent this time, so we can subtract that directly from 100
percent that gives us 73 percent. 73 percent of adults will not support
Universal Health Care. Unfortunately, figuring out the probability
of an event not happening is not always that easy.
Got a slightly more complicated question here. We have got 12,942 construction workers injured
by falling debris. A list of cities.
And a question is asking if an injured construction worker is selected at random.
What’s the probability the selected worker will have been injured in a city other than
Houston, Miami, or Denver? In other words what is the probability the
event did not take place in one of these three cities?
Let us start by adding up the numbers. We are given a total of 12,942 constructions
workers and we are given numbers of injuries. For Houston we are given 219, for Miami we
are given 112 and for Denver we are given 140.
So let us add those up. And that gives us 471 injuries that happened
in those places. In other words, 471 out of 12,942 injuries.
This is a fraction. If I divide through, I got a decimal and that
is .0364. This is the probability that an injury will
take place in one of those three cities. But we want the probability of it not happening.
So subtract from 1. That gives us 0.9636 and I am rounding to
four decimal places here. That is how to find the probability of an
event not happening. Check us out at StatisticsHowTo.com for more
videos and articles on everything elementary statistics.