Question 1082468
the formula for the binomial probability is:


p(x) = p^x * q^(n-x) * c(n,x)


when p = .6, q = .4 because q = 1 - p.


when x = 1 and n = 20, the formula becomes:


p(1) = .6^1 * .4^19 * c(20,1)


c(20,10) is the combination formula of c(n,x) = n! / (x!*(n-x)!)


when n = 20 and x = 1, this formula becomes c(20,1) = 20! / (1! * 19!)


this can be written as c(20,1) = (20 * 19!) / (1! * 19!)


simplify this to get c(20,1) = 20/1 = 20


p(1) = .6^1 * .4^19 * c(20,1) becomes p(1) = .6^1 * .4^19 * 20.


solve for p(1) to get p(1) = 3.298534883 * 10^(-7)


round this to 1 decimal digit and this becomes p(1) = 3.3 * 10^(-7)


multiply this by 100 to make it a percent and you get p(1) = 330 * 10^(-7)%


convert this to scientific format to get p(1) = 3.3 * 10^(-5)%


to convert to scientific format, there must be only 1 digit to the left of the decimal point


330 * 10^(-7)% has 3 digits to the left of the decimal point because the decimal point is implied after the 330.


it actually looks like 330. * 10^(-7)%


to get it to be 3.3, you have to divide 330 by 100 and multiply 10^(-7) by 100.


you would get p(1) = 3.3 * 10^(-7) * 100


10^(-7) * 100 is the same as 10^(-7) * 10^2 which results in 10^(-7+2) which results in 10^(-5)


you end up with p(1) = 3.3 * 10^(-5)%.


that looks like selection C.