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Statistics S1 Question!

An annual mathematics contest contains 15 questions, 5 short and 10 long. The probability that I get a short question right is 0.9.
The probability that I get a long question right is 0.5.
My performances on questions are independent of each other.

(iv) Find the probability that I get exactly 13 of the 15 questions right.

^^ please help, I'm stuck :frown:

Thanks

(p.s for those who have the mei book, its on page 177)
Original post by KanKan
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You want to start by splitting it into three cases depending on whether the two you get wrong are short or long questions, or a mixture.
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KanKan
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Original post by ghostwalker
You want to start by splitting it into three cases depending on whether the two you get wrong are short or long questions, or a mixture.


Awesome, thanks for the help :smile:
To get 13 correct, they have to achieve one of the following (i.e. the number of correct questions)(10 long AND 3 short) OR (8 long AND 5 short) OR (9 long AND 4 short) ==> (in other words, they have to get the 2/15 wrong both from the long questions or both from the short questions or 1 wrong from each set)It is of course Binomial... a bit long tooBoth wrong from long questions so all 5 short correct = (10C8 x 0.5^8 x 0.5^2) x (5C5 x 0.9^5 x 0.1^0) of course some parts here =1 but I have left them in for clarityBoth wrong from short questions so all 10 long correct = (5C3 x 0.9^3 x 0.1^2) x (10C10 x 0.5^10 x 0.5^0) as aboveOne wrong question from each set = (10C9 x 0.5^9 x0.5^1) x (5C4 x 0.9^4 x 0.1^1) as aboveAdding the results for the three rows = 0.02922

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