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Probability Questions 2A

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1. The function p(x) is the probability function for the random variable X. If p(1) = P(X=1) =.2, p(2)= P(X=2) = .1, p(3)=.3, f (7)=.1, and p(10)=.3. What is E(X)?
a. 3.4 b. 5.0 c. 9.8 d. 4.2

2. What is bigger C124 or C128? (Note: Cnk is the number of ways of choosing k things out of n.)
a. C124 b. C128 c. they're equal

3. Randomly choose one of the 225 people in a certain organization. What is the conditional probability the person chosen is a women given that you chose a smoker?
Men who smoke - 90 Men who don't spoke - 70
Women who smoke - 65 Women who don't smoke - 100
155 170
a. 65/155 b. 1 - 90/160 c. 65/165 d. 65/100

4. On a multiple choice test with three possible answers for each of the 15 questions, what is the probability that a student will get 6 correct just be guessing?
a. C156 (1/3)6(2/3)9 b. (1/3)6(2/3)9 c. (15/6)(1/3)6(2/3)9 d. none of these
b.
5. Same setup. What is the mean (the expected value) and the standard deviation, respectively, of the number of answers correct, a binomially distributed random variable?
a. 6, 2.54 b. 5, 1.83 c. 6, 1.33 d. 5, 3.33

6. A surgeon loses 9% of his patients; that is, they die. What is the probability that the first patient who dies will be his 5th surgery?
a. 3.9% b. 6.8% c. 7.3% d. 43.0% e. 6.2%
7. If a single bus always comes at a random time between noon and 2 PM and you arrive at the bus stop at 12:40, what is the probability you missed the bus?
a. 1/3 b. 1/ 4 c. 1/ 2 d. none of these

8. Two people, X and Y, predict the outcomes of 100 coin flips. X correctly predicts 52 of the 100 coin flips, and Y correctly predicts 31 of the 100 coin flips. Whose performance, X's or Y's, is most impressive? That is, most in need of an explanation?
a. X's b. Y's c. same for both

9. The lengths of pregnancies have a mean of 266 days and a standard deviation of 16 days. What is the probability a pregnancy lasts between 250 days and 298 days? No table needed.
a. 84.1% b. 68% c. 95% d. 81.5%

10. Same setup. A pregnancy lasts 284 days. What percentile of pregnancy lengths is in? That is, what percent of pregnancies last 284 or fewer days?
a. 84% b. 16% c. 87% d. 95%

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1. The function p(x) is the probability function for the random variable X. If p(1) = P(X=1) =.2, p(2)= P(X=2) = .1, p(3)=.3, f (7)=.1, and p(10)=.3. What is E(X)?
a. 3.4 b. 5.0 c. 9.8 d. 4.2

1*.2 + 2*.1 + 3*.3 + 7*.1 + 10*.3 = 5

2. What is bigger C124 or C128? (Note: Cnk is the number of ways of choosing k things out of n.)
a. C124 b. C128 c. they're equal

12 - 4 = 8

3. Randomly choose one of the 225 people in a certain organization. What is the conditional probability the person chosen is a women given that you chose a smoker?
Men who smoke - 90 Men who don't spoke - 70
Women who smoke - 65 Women who don't smoke - 100
155 170
a. 65/155 b. 1 - 90/160 c. 65/165 d. 65/100

There are 65 women smokers out of ...

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  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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  • "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "
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