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Math Help - How to figure out (at least) probability in Statistics?

  1. #1
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    How to figure out (at least) probability in Statistics?

    What is the probability that a student will answer at least two questions correctly by random guessing on an exam with 8 multiple-choice questions each of which as three options?

    What I don't get is the at least two questions correctly part. Do they mean P(2) + P(3) + P(4) +P(5) + P(6) + P(7) + (P8)?
    P(2) means 8C2 x (1/3)^2(2/3)^6 and ect....
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  2. #2
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    At least one is the oppsite of none: 1-P(none)
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  3. #3
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    So what do they want you to do when they say at least two?
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  4. #4
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    The answer I came up with is 0.804907788. Can anybody confirm that I did it correctly?
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  5. #5
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    Hello, krzyrice!

    The answer I came up with is 0.804907788.
    Can anybody confirm that I did it correctly?
    That's the answer I got!

    I did it by using the "opposite" approach.
    The opposite of "at least two" is "less than two" (zero or one).

    P(0) \:=\:_8C_0(\tfrac{1}{3})^0(\tfrac{2}{3})^8 \:=\:0.039018442<br />

    P(1) \:=\:_8C_1(\tfrac{1}{3})^1(\tfrac{2}{3})^7 \:=\:0.156073769<br />

    . . Hence: . P(0\text{ or }1) \:=\:0.039018492 + 0.156073769 \:=\:0.195092211


    Therefore: . P(\text{at least 2}) \;=\;1-0.195092211 \;=\;0.804907789

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  6. #6
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    Thank you so much for your help! You are a great mathematician and now I have more confidence in getting that A on the test tomorrow.
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