The probability of winning on an arcade game is 0.568. If you play the arcade game 22 times, what is the probability of winning

Question

2 years ago

12

more than 15 times

1 answer:

Serggg [28] · Answer 1 · 2023-08-05T16:07:26+03:00

The probability of winning 15 out of the 22 games is $P = 0.099$

<h3>what is the probability of winning more than 15 times?</h3>

We know that the probability of winning on the arcade game is 0.568.

Then the probability of losing is:

P = 1 - 0.568 = 0.432

The probability of winning 15 out of 22 games is given by the equation:

$P = C(22, 15)*(0.568)^{15}*(0.432)^{7}$

Where C(22, 15) is the number of combinations of 15 elements that we can make with a set of 22 elements, given by:

$C(22, 15) = \frac{22!}{(22 - 15)!*15!} = \frac{22!}{7!*15!} = \frac{22*21*20*19*18*17*16}{7*6*5*4*3*2*1} = 170,544$

Then the probability is:

$P = 170,544*(0.568)^{15}*(0.432)^7 = 0.099$

If you want to learn more about probability:

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