Probability and Statistics > Probability > How to calculate the probability of an event NOT happening

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## How to calculate the probability of an event NOT happening: Overview

Probability questions are often word problems that appear more difficult than they actually are. The trick is to identify the type of problem you have. This article will tell you how to

**find the probability**of a simple event

**not**happening. You can also check out the Probability Index for more question types.

## How to calculate the probability of an event NOT happening: Steps

**Step 1:***Choose one of the following sample questions below that most closely matches your problem and go to the step indicated.*Pay particular attention to the**bold**words when selecting.- In a certain year, 12,942 construction workers were injured by falling debris. The top six cities for injuries were: New York 141, Houston 219, Miami 112, Denver 140, and San Francisco 110. If an injured construction worker is
**selected at random**, what is the probability that the selected worker will have been injured in a city**other than**Houston, Miami, or Denver?*If your problem looks like this, go to step 2.* - If the
**probability**that a major hurricane will hit Florida this year is 0.49, what is the**probability**of a major hurricane**not**hitting Florida this year?*If your problem looks like this, go to step 5.* - Twenty seven
**percent**of American adults support Universal Health Care. If an American adult is chosen at random, what is the probability they**will not**support Universal Health Care?*If your problem looks like this, go to step 6.*

- In a certain year, 12,942 construction workers were injured by falling debris. The top six cities for injuries were: New York 141, Houston 219, Miami 112, Denver 140, and San Francisco 110. If an injured construction worker is

**Step 2:***Add up the given cities.*

Houston (219) + Miami (112) + Denver (140) =**471****Step 3:***Divide the number you found in step 2 by the total number of people or items given*. In this case, we were told that 12,942 construction workers were injured. So:

471 / 12,942 =**.0364**.**Step 4:***Subtract the number you found in step 3 from 1 (that is, the number one, not step 1).*

1 – .0364 =**0.9636**(rounded to four decimal places).You’re done!**Step 5:***Subtract the “not” probability from 1*.

1 – 0.49 =**0.51**. That’s it!**Step 6:***Convert the percentage to a decimal*.

Twenty seven percent =**0.27****Step 7:***Subtract the number in step 6 from 1 (that is, the number one not step 1!)*.

1 – 0.27 =**0.73**.That’s it–you’re done!

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Probability of an event NOT happening was last modified: October 15th, 2017 by

Suppose A and B are events with p(A)=0.24, p(B)=0.42 and p(AnB)=0.12. What is the probability of A does not occur. B does not occur.

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