What is the probability that exactly 2 of the 20 males are colorblind? (Note: Some answers are rounded.)?

This is what is given:





Colorblindness is any abnormality of the color vision system that causes a person to see colors differently than most people or to have difficulty distinguishing among certain colors (www.visionrx.xom).





Colorblindness is gender-based with the majority of sufferers being males.





Roughly 8% of white males have some form of colorblindness, while the incidence among white females is only 1%.





A random sample of 20 white males and 40 white females was chosen.





Let X be the number of males (out of the 20) who are colorblind.





Let Y be the number of females (out of the 40) who are colorblind.





Let Z be the total number of colorblind individuals in the sample (males and females together).





Answers:


(a) .08


(b) .2711


(c) .0143


(d) .5422


(e) .0159

What is the probability that exactly 2 of the 20 males are colorblind? (Note: Some answers are rounded.)?
The answer is b)





Let X be the number of white males who are color blind. X has the binomial distribution with n = 20 trials and success probability p = 0.08





In general, if X has the binomial distribution with n trials and a success probability of p then


P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)


for values of x = 0, 1, 2, ..., n


P[X = x] = 0 for any other value of x.





The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.


Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.





X ~ Binomial( n , p )





the mean of the binomial distribution is n * p = 1.6


the variance of the binomial distribution is n * p * (1 - p) = 1.472


the standard deviation is the square root of the variance = √ ( n * p * (1 - p)) = 1.21326





The Probability Mass Function, PMF,


f(X) = P(X = x) is:





P( X = 0 ) = 0.1886933


P( X = 1 ) = 0.3281623


P( X = 2 ) = 0.2710906 ← answer


P( X = 3 ) = 0.1414386


P( X = 4 ) = 0.05227078


P( X = 5 ) = 0.01454491


P( X = 6 ) = 0.003161937


P( X = 7 ) = 0.0005499022


P( X = 8 ) = 7.770357e-05


P( X = 9 ) = 9.00911e-06


P( X = 10 ) = 8.617409e-07


P( X = 11 ) = 6.812181e-08


P( X = 12 ) = 4.442727e-09


P( X = 13 ) = 2.377379e-10


P( X = 14 ) = 1.033643e-11


P( X = 15 ) = 3.59528e-13


P( X = 16 ) = 9.769782e-15


P( X = 17 ) = 1.998932e-16


P( X = 18 ) = 2.897004e-18


P( X = 19 ) = 2.651719e-20


P( X = 20 ) = 1.152922e-22
Reply:well the answer to the question in your title thing


you 2 over 20 and multiply them by 5 because there is 5 20s in 100. But you have to do the same thing to the numerator. So 2 times 5 equals 10 so your answer in a fraction is 10 over 100 which equal to 10%.
Reply:The answer is (b).


the formula to solve this is:


((20!)/ (2!*(20-2)!) )* ((.08) ^2 )*(0.92^(20-2))


if you want explanation of formula please repost or something...
Reply:P(2m) = P(Exactly 2 of 20 males colorblind)





P(2m) = (20C2)(.08)²(1 - .08)^(20-2)





= 190*(.08)²(.92)^18 ≈ 0.27109


___________





The answer is (b) .2711.