The probability of winning 15 out of the 22 games is [tex]P = 0.099[/tex]
what is the probability of winning more than 15 times?
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:
[tex]P = C(22, 15)*(0.568)^{15}*(0.432)^{7}[/tex]
Where C(22, 15) is the number of combinations of 15 elements that we can make with a set of 22 elements, given by:
[tex]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[/tex]
Then the probability is:
[tex]P = 170,544*(0.568)^{15}*(0.432)^7 = 0.099[/tex]
If you want to learn more about probability:
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