1) Suppose that 25% of students at a particular college have SATscores over 1200
ID: 2953593 • Letter: 1
Question
1)Suppose that 25% of students at a particular college have SATscores over 1200. If I pick 5
students at random from this student body, what is the probabilitythat at least one of
those picked have SAT scores over 1200?
2)
Each of two cabinets identical in appearance has 2 drawers. CabinetA contains a silver coin
in each drawer, and cabinet B contains a silver coin in one of itsdrawers and a gold coin in
the other. A cabinet is randomly selected, one of its drawers isopened, and a silver coin is
found. What is the probability that there is a silver coin in theother drawer?
Please help with one or both if you know how to solve!
Explanation / Answer
This is a typical case of binomial distribution where successof a trial is student having SAT score > 1200. and n = 5. with p= 0.25
therefore we want P(x >= 1) = 1-P(x=0) = 1-nC0 p0 (1-p)(5-0) = 1-1*1*0.755 =1 - 0.2373 = 76.27%
b) Let A: picking up the cabinet with silver coin in both thedrawers
B: Finding a silver coin.
now if you see we want P(A|B) = P(AB)/P(B)
P(AB) = Probability that we pick the cabinet withsilver coin in both drawers * probability of picking a silver coinfrom that drawer = (1/2)* (2/2) = 0.5
P(B) = Probability of picking a silver coin
this can happen in two ways. 1) you pick the cabinet with bothsilver coins you automatically get a silver coin...2) you pickcabinet with one silver coin and pick that silver coin.
= P(A)*P(B|A) +P(A')*P(B|A') = 0.5*1+0.5*0.5 = 0.5+0.25 =0.75
therefore P(A|B) = 0.5/0.75 = 33.33%
Hope this is helpful. Feel free to ask for anyclarifications.
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