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November 16th, 2008, 03:24 PM   #1
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Probability problems I'm stumped at

Just a quick backround, I'm taking math 156 probability at the CSU math testing center. They allow you 4 tries of randomized tests and select your best score until after the deadline. I had 3 attempts 0/12(I mostly just left to see the correct answers and use it as a second study guide), 7/12, and 8/12. I'm on my last attempt tommorrow and have studied all the problems and understood most but three.

Problem 1: two dice are thrown and the sum of the number of dots on the dice are noted. The probability that the sum is 12 given that the sum is even is closest to
correct answer: .056 You get this by 2/36 however I put down .028 doing 1/36 because you could only get 12 with (6,6) and that counts as a single unlike (2,3) or (3,2)
My question is does (6,6) get counted twice? Because I remember a problem similar with numbers less than 7 and (1,1) was counted once

problem 2: compute the proability that a five letter word made from any letters of the alphabet starts and ends with the same letter. Round your answer to six digits after the decimal point. That last(rightmost) digit in the answer is
correct answer: 2
however I put down 9 with 1/26 * 1 * 1 * 1 * 1/26 Don't understand how they got 2.

Problem 3: compute the probability that a five letter word made from any letters of the alphabet contains at least one vowel. Round your answer to six digits after the decimal point. The last(rightmost) digit in the answer is:
correct answer: 0
I put down 8 with 5/26 Don't understand how the got 0
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November 16th, 2008, 05:49 PM   #2
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Problem 1: There are eighteen results to consider (since the sum is even), and you can reasonably assume they are equally likely. One of them is (6, 6).

Problem 2: You can reasonably ignore much of the detail. What is the probability that the fifth letter is the same as the first? There are twenty-six possibilities for the fifth letter, and you can reasonably assume they are equally likely. Only one of them is the same as the first letter.

Problem 3: What is the probability that the word doesn't contain any vowel?
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November 21st, 2008, 05:54 PM   #3
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Re: Probability problems I'm stumped at

Quote:
Originally Posted by skipjack
Problem 3: What is the probability that the word doesn't contain any vowel?
1?
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November 22nd, 2008, 09:18 AM   #4
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No. Any letter is possible and each letter has a 21/26 chance of being a consonant, so what is the probability that all five are consonants? When you've found that, subtract it from 1, then round the result to 6 decimal places and note the last digit of the result.
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November 22nd, 2008, 12:46 PM   #5
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Re: Probability problems I'm stumped at

Thanks!

1 - (21^5)/(26^5) = .656260?
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