Expected Value and Standard Error question?

NetherCraft 0

A letter is drawn 1,000 times, at random, from the word A R A B I A. There are two offers:

(A) You win $1 if the number of A’s among the draws is 10 or more above the expected number.

(B) You win $1 if the number of B’s among the draws is 10 or more above the expected number.

I know I should make box models for each, but how would they look like? Do each letter count for different numbers? So in this case, I wouldn’t be able to use the “short-cut” method for finding the S.D.? For the first one I’m thinking three boxes with “1” which counts for the letter “A” (since there’s 3 of 6 letters), so then “0” would count for the other numbers? Is this right? Thanks!

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1 Answer

  • cinéphile

    A letter is drawn 1,000 times, at random, from the word A R A B I A. There are two offers:

    These are BOTH Binomial distributions and can be solved using a Binomial calculator …

    http://stattrek.com/online-calculator/binomial.asp…

    (A) You win $1 if the number of A’s among the draws is 10 or more above the expected number.

    expected = np = 1000(3/6) = 500

    Now, using the Binomial calculator …

    P(X ≥ (500+10) = 0.274

    (B) You win $1 if the number of B’s among the draws is 10 or more above the expected number.

    expected = np = 1000(1/6) = 167

    Now, using the Binomial calculator …

    P(X ≥ (167+10) = 0.201

    Your decision should be to choose game A since the probability of 10 or more above expected is 0.274

    hope that helped


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