Answer:
0.021739
Step-by-step explanation:
This situation can be modeled with the Binomial Distribution which gives the probability of an event that occurs exactly k times out of n, and is given by
[tex]\large P(k;n)=\binom{n}{k}p^kq^{n-k}[/tex]
where
[tex]\large \binom{n}{k}[/tex]= combination of n elements taken k at a time.
p = probability that the event (“success”) occurs once
q = 1-p
In this case, the event “success” is winning the roulette game with probability 1/36 = 0.027777 and n=100 rounds.
The probability value of winning the roulette game 7 or more times out of 100, is
P(7;100)+P(8;100)+...+P(100;100) =
1 - P(0;100)+P(1;100)+...+P(6;100)
We can find the sum of these last 7 terms either by hand or computer-assisted and we would find
P(0;100)+P(1;100)+...+P(6;100) =
[tex]\large \binom{100}{0}0.027777^0*0.972222^{100}+\binom{100}{1}0.027777^1*0.972222^{99}+...+\\\binom{100}{100}0.027777^{100}*0.972222^0=0.978261[/tex]
and the p-value (probability value) for winning 7 or more out of 100 rounds is
1-0.978261 = 0.021739
