I was thinking today that if something with a probability of occurring of 1% happened 100 times, the

Bruno Pittman

Bruno Pittman

Answered question

2022-07-08

I was thinking today that if something with a probability of occurring of 1% happened 100 times, then the probability of that something happening is 100%, I believe that according to the addition rule for probabilities the probabilities for each event should be added up to get the total probability thus 1/100 + 1/100 + 1/100 ... up to 100 = 100/100 = 1 = 100%.

Now, there's still the possibility that the event didn't occur any one of those 100 times when it could have, because each time is independent. If such is the case, then obviously the probability is not 100%.

I believe I'm wrong and that I'm doing something wrong. So I would very much appreciate any guidance as to how to go about calculating the probability of something that happens 100 times that has a chance of occurring of 1% every time. For example, let's say there's a probability of 1% of dying from eating too much Cap'n Crunch, if I ate too much Cap'n Crunch 100 times, what is the probability that I will die?

Answer & Explanation

verzaadtwr

verzaadtwr

Beginner2022-07-09Added 17 answers

Think about it this way: The probability of not happening is .99, so each time, p = p x 0.99. P of never happend in 100 times is 0.99 ^ 100 = 0.366. Finally, the probability of a 1% 100 times happened at least once is 0.63.
Wade Bullock

Wade Bullock

Beginner2022-07-10Added 5 answers

In order to calculate the probability of at least one successful experiment out of n experiments, you should calculate 1 minus the probability of the complementary event (i.e., 1 minus the probability of no successful experiment out of n experiments).

The general formula is 1 ( 1 p ) n , where p is the probability of success in a single experiment.

In your question p = 0.01 and n = 100, hence the answer is 1 ( 1 0.01 ) 100 63.39 %.

It is worth noting that in order for this method to be correct, the experiments must be independent of each other (i.e., the result of any experiment must not impact the result of any other experiment).

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