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A test consists of fifteen true/false questions. A student who forgot to study guesses randomly on every question. What is the probability that the student answers exactly five questions correctly?

 Mar 22, 2020
 #1
avatar+485 
+2

First, the number of ways to choose 5 questions out of 15 is equivalent to 

 

\(15 \choose 5 \)\(15!/(10!*5!) = 15*14*13*12*11/(5*4*3*2*1)\)

Canceling out top and bottom, we get:

\(3*7*13*11 = 3003\)

 

Next, we need the probability that he gets exactly five questions, which is:

\((1/2)^5\)

However, we haven't accounted for the next 10 questions which he needs to get wrong, which is a probability of 

\((1/2)^{10}\)

 

Our answer is then:

\(3003*{1/2}^5*{1/2}^{10} = 3003/(2)^{15}\approx 0.0916442871\)

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 Mar 22, 2020
edited by jfan17  Mar 22, 2020
 #2
avatar+1968 
+2

Nice, jfan17!!!

CalTheGreat  Mar 22, 2020
 #3
avatar+109524 
+1

Nice work Jfan17 .... except you forgot some brackets.  Can you work out where and fix it?

 

Brackets are very important.  wink

 Mar 22, 2020
 #4
avatar+485 
+2

Oh I see where! Thanks for reminding me melody! 

 Mar 22, 2020
 #5
avatar+109524 
0

That is much better now :)

Melody  Mar 22, 2020

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