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February 23rd, 2019, 08:53 AM  #1 
Newbie Joined: Feb 2019 From: Canada Posts: 2 Thanks: 0  Probability Question
Hello folks, Just a relatively simple question based on nothing but my own curiosity. I'm simply not certain of the equation involved to figure it out for myself. What are the odds, given a binary choice, that someone could accurately guess 19/22 answers correctly? Thanks in advance! 
February 23rd, 2019, 09:12 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,373 Thanks: 1275 
Assuming you have a 50% chance of guessing correctly, and assuming you mean exactly 19 out of 22 correct guesses $p= \dbinom{22}{19}\left(\dfrac 1 2\right)^{22} = \dfrac{385}{1048576} \approx 0.000367165$ The odds are $\dfrac{385}{1048576385} = \dfrac{385}{1048191} \approx 0.0003673$ So not very likely. 
February 23rd, 2019, 09:23 AM  #3 
Newbie Joined: Feb 2019 From: Canada Posts: 2 Thanks: 0 
Those are the assumptions, yes. I had argued that the likelihood was quite small, but could not back it up with stats. Thank you, sir. 
March 5th, 2019, 12:49 PM  #4 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 637 Thanks: 85 
Use https://stattrek.com/onlinecalculator/binomial.aspx for any problems with a number of successes, number of trials, and probability that is constant. It works for items picked with replacement. If items are picked without replacement, the probability changes based on what has been picked already. In that case, the probability can be calculated, but not by what I linked to.


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