Posted by carol on .
In a certain state, it has been shown that only 56% of the high school graduates who are capable of college work actually enroll in colleges.Find the probability that, among the 11 capable high school graduates in this state, each number will enroll in college.
a. Exactly 7
b.All 11
c.At least 4
d. Exactly 2
e. Less than 3
f None

math 
bobpursley,
I wonder how anyone can measure who is capable of college work? Exactly what is "college work" anyway? From my observation of all these online students enrolled in "colleges", being told they are doing "college work", and getting "degrees", one wonders.
I have seen a number of online colleges (want me to list them?) whose students are performing at less than high school level, yet getting "college credit" for it. An it amazes me how these "colleges" backscratch each other in giving each other "accrediation" to one another.
Enough, but it is a worthy question.
Here Pr(each)=.56, so if each kid makes independent decisions..., and the probability for a kid not going to college is .47
Pr(7)=.53^7*.47^4 * ways to do this, or
ways to do this (selecting 7 out of 11)
= 11!/(7!4!)
SO the final answer to your question..
Pr(7 of 11)=.53^7*.47^4*11!/(4!*7!)= nice math problem. Enter this into your google search window:
.53^7*.47^4*11!/(4!*7!)=
check my logic.. 
math 
bobpursley,
I did the exactly 7, follow my steps to get the others. On the less than three, do zero first, then exactly1, and exactly 2, then add those to get less than three.

math 
Steve,
Good logic, but I wonder about the .47 in light of P(college) = .56