SOLUTION: A true/false test has 4 questions. What is the probability of getting at least 3 right by guessing the answers randomly?

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Question 1042801: A true/false test has 4 questions. What is the probability of getting at least 3 right by guessing the answers randomly?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
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A true/false test has 4 questions. What is the probability of getting at least 3 right by guessing the answers randomly?
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The full space of outcomes has  2%5E4 = 16 elements.

The successive outcomes are  (a) 4 matching of 4 (only one),  and  (b) 3 matching of 4 (4 possibilities).

Hence,  the answer is  %281%2B4%29%2F16 = 5%2F16 = 0.3125.


Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!
A true/false test has 4 questions. What is the probability of getting at least 3 right by guessing the answers randomly?
Probability of getting at least 3 means the probability of getting 3 or the probability of getting 4 correct. 

Use the BINOMIAL PROBABILITY formula: %22+%22%5Bn%5DC%5Bs%5D+%2A+p%5Es+%2A+q%5E%28n+-+s%29

Probability of getting 3 correct:  

Probability of getting 4 correct:  

Probability of getting at least 3 correct (probability of getting 3 or 4 correct): highlight_green%28matrix%281%2C3%2C+.25+%2B+.0625%2C+or%2C+highlight%28.3125%29%29%29

OR

Use the BINOMCDF feature on a calculator (e.g. TI-83/84). Enter: binomcdf(4,.5,1). You should also get highlight%28.3125%29

OR

Use MS Excel. Enter: "=1-binomdist(3-1,4,.5,1." You should also get the above answer.