# Multiple questions in probability and statistics

Can you please provide step by step instruction on how to work these problems? I have tried to worked them out, but do not get the answers posted. Attached are the problems. Thanks!

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See the attached file.

27. Suppose 2 cards are drawn without replacement from an ordinary deck of 52. Find the probabilities of the following results. (Answer: .9955)

At most one is a queen.

Note that first card can be drawn in 52 ways and second in 51 ways. So total ways = 52 x 51

Since there are 4 queens in a pack, First queen can be drawn in 4 ways and the next in 3 ways. So total ways to pick 2 queens = 4 x 3 = 12.

The chance that both cards are queens = (4 x 3)/ (52 x 51) = 0.00452488

Chance of at most 1 queen = 1 - 0.00452488 = 0.9955 nearly

47. In placebo-controlled trials of Prozac®, a drug that is prescribed to fight depression, 23% of the patients who were taking the drug experienced nausea, whereas 10% of the patients who were taking the placebo experienced nausea.*

a. If 50 patients who are taking Prozac® are selected, what is the probability that 10 or more will experience nausea?

b. Of the 50 patients in part a, what is the expected number of patients who will experience nausea?

c. If a second group of 50 patients receives a placebo, what is the probability that 10 or fewer will experience nausea?

d. If a patient from a study of 1000 people, who are equally divided into two groups (those taking a placebo and

those taking Prozac), is experiencing nausea, what is the probability that he/she is taking Prozac?

e. Since .23 is more than twice as large as .10, do you think that people who take Prozac® are more likely to experience nausea than those who take a placebo? Explain.

(Answers: a. about .74 b. about 12 c. about .99 d. about .70)

The distribution in this case is a binomial distribution.

The binomial distribution consists of n trials and p, the probability of success in each trial. Chance of exactly

k successes = (n choose k) p^[k](1 - p)^[n-k]

Where ^ means raised to the power of.

(n choose k) = n! / (k! (n - k)!) where ! means factorial.

a) Probability of nausea = 0.23

Chance that exactly k patients experience nausea is given by:

(50 choose k) x 0.23^k x (1 - 0.23) ^ (50 - k) where ^ means raised to the power of.

Since we want the probability for k >= 10, we sum ...

#### Solution Summary

Probability of card drawing

Binomial distribution

Probability in Lottery

Statistics: Five Probability multiple choice questions

1. A kindergarden class consists of 14 boys and 11 girls. If the teacher selects children from the class using random sampling:

a. what is the probability that the first child selected will be a girl?

b. if the teacher selects a random sample of n=3 children and the first two children are both boys, what is the probability that the third child selected will be a girl?

2. For each of the following z-scores, sketch a normal distribution and draw a vertical line at the location of the z-score. Then determine whether the body is to the right or left of the line and find the proportion in the body.

a. z= 0.75

b. z= -1.40

c. z= 0.85

d. z= -2.10

3. the distribution of IQ scores is normal with mean= 100 and standard deviation =15

What proportion of the population has IQ scores?

a. greater than 115?

b. greater than 130?

c. greater than 145?

4. A multiple choice test has 48 questions each with four response choices. If a student is simply guessing at the answers

a. what is the probability that a student would get more than 18 answers correct simply by guessing?

5. A trick coin has been weighted so that heads occurs with a probability of p=2/3, and p(tails) = 1/3. Iif you toss this coin 72 times

a. how many heads would you expect to get on average?

b. what is the probability of getting more than 50 heads?

c. what is the probability of getting exactly 50 heads?