SOLUTION: I need help with my probability and statistics homework. Can someone please show me how to do these problems: 7. A college dome houses 100 freshmen, 80 sophomores, and 60 junior

Question 467769: I need help with my probability and statistics homework. Can someone please show me how to do these problems:
7. A college dome houses 100 freshmen, 80 sophomores, and 60 juniors. 30 of the freshmen, 20 of the sophomores, and 10 of the juniors are from Arkansas. If a randomly chosen student is from Arkansas, what is the probability that this student is a freshman?
C(100,30)?
8. A box contains 3 red balls and 5 white balls. You draw two balls in succession, without replacement (i.e., the balls drawn are not put back into the box). Use a tree diagram to find the probability that the balls you draw are a white ball followed by a red ball. Answer in fraction reduced to the lowest terms.
c(8,5) x c(7,3)?
9. You are given 5 keys, one of them opens a chest. Not knowing which key is the right key, you try them one by one. Find the probability that the third key you try opens the chest. Use a tree diagram to solve this problem. What do you think is the probability that the fourth key opens the chest? And the fifth key? Answer in fraction reduced to the lowest terms.
3rd key: c(5,3)?
10. A fair coin is flipped three times. Given that the first two flips resulted in heads, what is the probability that the third flip is a tail?
(A) 1/8 (B) 7/8 (C) 3/4 (D) 1/2
D?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
7. A college dore houses 100 freshmen, 80 sophomores, and 60 juniors. 30 of the freshmen, 20 of the sophomores, and 10 of the juniors are from Arkansas. If a randomly chosen student is from Arkansas, what is the probability that this student is a freshman?
P(frosh | from Arkansas) = 30/60 = 1/2
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8. A box contains 3 red balls and 5 white balls. You draw two balls in succession, without replacement (i.e., the balls drawn are not put back into the box). Use a tree diagram to find the probability that the balls you draw are a white ball followed by a red ball. Answer in fraction reduced to the lowest terms.
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P(white and red) = P(red | white)*P(white) = (3/7)*(5/8) = 15/56
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9. You are given 5 keys, one of them opens a chest. Not knowing which key is the right key, you try them one by one. Find the probability that the third key you try opens the chest. Use a tree diagram to solve this problem. What do you think is the probability that the fourth key opens the chest? And the fifth key? Answer in fraction reduced to the lowest terms.
3rd key: c(5,3)?
---
P(not,not,yes) = (4/5)(3/4)(1/3) = (3/5)(1/3) = 1/5
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P(not,not,not,yes) = (4/5)(3/4)(2/3)(1/2) = (3/5)(1/3) = 1/5
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P(not,not,not,not,yes) = (4/5)(3/4)(2/3)(1/2)1 = 1/5
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10. A fair coin is flipped three times. Given that the first two flips resulted in heads, what is the probability that the third flip is a tail?
Ans: Results are independent ans = 1/2
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(A) 1/8 (B) 7/8 (C) 3/4 (D) 1/2
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Cheers,
Stan H.
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