geico: If I have understood your question corre..

Posted by: geico September 10, 2009

If I have understood your question correctly it can be modeled with binomial distribution.

Part a).

The probability function of Y is:

f(y) = (n choose y)*p^y*(1-p)^(n-y)

where 0 =< y =< 4, n = 4, and probability of choosing new formula (p) = 1/2

Part b).

P( Y => 3) = 1 - P(Y =< 3)

P(Y =< 3) = Summation {f(y)}

Part c).

E(Y) is mean of Y and mean of binomial distribution is n*p

E(Y) = np

Part d).

Variance of binomial distribution is n*p*(1-p)

Now you plug in the numbers and you should get the answers. I hope that helps... good luck with that!