Question 866735: 20% of the population in Turkey is estimated to have green eyes. Out of a random group of 11 people in Turkey, what is the probability that exactly 4 have green eyes?
Round the percentage to the nearest whole number.
I got 40 when I did this. Is that correct? If not, how would I solve this type of equation?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! You use the formula
(n C k)*(p)^(k)*(1-p)^(n-k)
Note: n C k is found through the combination formula
In this case,
n = 11 (sample size)
p = 0.2 (probability of success, in this case, probability of picking someone with green eyes)
k = 4 (number of exact successes you want)
So you'd have
(n C k)*(p)^(k)*(1-p)^(n-k)
(11 C 4)*(0.2)^(4)*(1-0.2)^(11-4)
0.1107296256
You would use a calculator to evaluate to get the last line shown above. That means we'd have a 0.1107296256*100 = 11.07296256% chance of picking exactly 4 people with green eyes.
So the answer is actually 11% (and not 40%)
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