90 students will graduate from Lima Shawness High School this year. Out of the 90, 50 are planning to attend college. Two students are selected at to carry the flag at graduation. What is the probability that both of them are planning to attend college?

Question

90 students will graduate from Lima Shawness High School this year. Out of the 90, 50 are planning to attend college. Two students are selected at  to carry the flag at graduation. What is the probability that both of them are planning to attend college?

Anthony Amato · Accepted Answer

#P("picking 2 people as flag bearers who are also going on to college")=2450/8010~=0.306#

We can divide the number of ways to select 2 from a pool of 90 (the entire graduating class) by the number of ways to select 2 from a pool of 50 (the members of the graduating class going to college).

We'll be using the combinations formula because we don't care in what order the two people are picked:

#C_(n,k)=(n!)/((k!)(n-k)!)# with #n="population", k="picks"#

And so:

#(C_(50,2))/(C_(90,2))=((50!)/(2!48!))/((90!)/(2!88!))=>#

#=>(50!)/(cancel(2!)48!)(cancel(2!)88!)/(90!)=>#

#=>(50xx49xxcancel(48!))/(cancel(48!))(cancel(88!))/(cancel(88!)xx89xx90)=>#

#=>2450/8010~=0.306#

And so:

#P("picking 2 people as flag bearers who are also going on to college")=2450/8010~=0.306#