The question: A baseball player has a 5% chance to hit a homerun each at bat. If the player is up 4 times, what is the chance he hits 2 or more homeruns. I came up with the answer, but this was a long process. I need a formula. And is there an easier way of counting the possibilities?(adsbygoogle = window.adsbygoogle || []).push({});

I did it like this:

Probability of 0 out of 4 + 1 out of 4 = 1.401875

Probability of 0 out of 4 is (0.95)(0.95)(0.95)(0.95)(1) with 1 possibility

Probability of 1 out of 4 is (0.05)(0.95)(0.95)(0.95)(4) with 4 possibilities so

The other 11 possibly scenarios are 6 to do 2 out of 4, 4 to do 3 out of 4, and 1 to do 1 out of 4, for a total of 16 (4x4) but is there an easier way than counting these?

Thank you!

EDIT: for 'player' :)

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# Probability equation

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