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Help with probability?
There is a class of 315 students taking a T/F quiz of 10 questions. We would normally think it unlikely that a student would get at most 2 questions right out of 10 by flipping a coin, but with a class this large, it might be possible. Here we’ll calculate the probability of at least one student in the class of size 315 getting at most 2 questions right.
What is the probability of every student in the class getting 3 or more questions right?
What is the probability of some student in the class getting at most 2 questions right?
1 Answer
- PhilipLv 68 years agoFavorite Answer
At most 2 means 0,1,and 2.
P(0) = .5^10 = .00098
P(1) = 10*.5^10 = .0098
P(2) = 10C2*.5^10 = .0439
P(0,1,2) = .0547
With a 50/50 chance of being right, the expected number of correct answers by flipping a coin is 5.
This is confirmed by the low probability of only getting at most 2 correct.
3 or more questions correct is the compliment of at most 2 correct so...
P(3 or more) = 1 - .0574 = .9426
As an FYI, the probability of getting exactly 5 correct is...
P(5) = 10C5*.50^10 = .2461
