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 “shortcut” 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!
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/onlinecalculator/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