In​ 5-card poker, the number of outcomes favorable to an event E is given in the table. Find the probability of being dealt a full house.

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Consider the situation where you have a bag that contains 8 black marbles and 2 white marbles. You take a marble from the bag; you record whether it is black or white, and put it back in the bag before you take another marble from the bag. You do this 10 times. What is the probability that you will draw the same number of black and white marble?

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Suppose you are investigating whether there is a difference in taste between organic milk and regular milk. You recruit 16 random volunteers and ask each one individually after tasting to tell you which of two unmarked glasses contains the organic milk. Let X be the number of correct guesses. If there really were no difference in taste between organic milk and regular milk, what would be the probability of exactly six correct guesses, to three decimal points?

A survey reported that

3232​%

of people plan to spend more on eating out after they retire. If

tenten

people are randomly​ selected, determine the values below.

Many variables in medicine follow a normal distribution where there are approximately an equal number of values below the mean as above the mean. Describe two variables that would probably follow a normal distribution. Also note which of the two variables would be likely to have a larger standard deviation and why.

As an alternative question, what are some other potential probability distributions in the health care field such as bimodal, skewed, or exponential and give variables that would probably follow that distribution.

For a binomial probability distribution, n = 130 and p = 0.60. Let x be the number of successes in 130 trials. a. Find the mean and standard deviation of this binomial distribution.

a. Find the mean and the standard deviation of this binomial distribution.

b. Find to 4 decimal places P(x ≤ 75) using the normal approximation. P(x ≤ 75) =

c. Find to 4 decimal places P(67 ≤ x ≤ 72) using the normal approximation. P(67 ≤ x ≤ 72) =

1. Consider the following function: (?) = ?(?³ + 1), ? = 0, 1, 2, 3
2. 1. What is the value of the constant ? so that (?) is a pmf?
   2. Plug-in the value of ? in the expression of (?) and show the pmf in a table. Draw a probability histogram of the pmf.
   3. Find the cdf (?) and write it explicitly defined over the entire real number line. Draw the cdf (?).
   4. Calculate the probabilities: (i). (0 < ? ≤ 2),      (ii) ?(? ≠ 1).
   5. Find the expected value of ?.
   6. Find the expected value of 3?³ − 2? + 1.
   7. Find the variance of ?.

Alex met Claire Boucher (Grimes) at McGill. He has been waiting for the release of her next album. Assume that the waiting time is exponential with mean 3 years. To keep up with releases Alex receives Resident Advisor’s monthly album review newsletter. Assume that the album will be featured in the next issue after its release. Let X be the number of newsletters required to get news of the release of the album. Find the probability mass function of X.

The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200​ minutes, with the results shown in the table below. Complete​ (a) through​ (c) to the right.

Arrivals, Frequency

0 13

1 25

2 47

3 40

4 32

5 23

6 12

7 6

8 2

Compute the standard deviation.

What is the probability that there will be fewer than 2 arrivals in a given​ minute?

The number of men and women wearing hats at a recent baseball game is recorded. The results are shown below. Hat No Hat Total Men 35 21 46 Women 10 32 42 Total 45 53 88 If one of these people at the baseball game is selected at random, find the probability that a) the person is a woman b) the person was wearing a hat. c) the person was wearing a hat, given that the person was a man. e) the person is a man, given that they were not wearing a hat.