# Probability Question

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An event has an 8% chance to occur per try. How would I calculate the chance of the event occurring at least once after 3 tries?

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Is the probability in one trial independent of the actual results in the others?

If so, can you write a formula for the event to not occur at all in three tries?

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An event has an 8% chance to occur per try. How would I calculate the chance of the event occurring at least once after 3 tries?

The chance of it not occurring in 3 tries is $$0.92^3$$
So, you want $$1- 0.92^3$$

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To gain some insight into this problem, try the following brute-force method. List all the possible outcomes for the set of three tries:

1=no, 2=no, 3=no : probability = 0.92 * 0.92 * 0.92 = …
1=yes, 2=no, 3=no : probability = 0.08 * 0.92 * 0.92 = …
etc.

Enumerate all the outcomes (how many of them are there?), calculate the probability for each one, and add up the ones that meet your criterion.

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Staff Emeritus