1. )A special deck of cards consists of  541 cards,  66 of which are red;  the rest are black. If a card is selected at random and you look at it and remember what it is or write it down, then you  replace it into the same deck, shuffle the deck at least 7 times, then select a card. 7 shuffles is an adequate number to thoroughly mix the cards and prevent any doubts,   Find the probability that both cards are red.  leave answer as an unreduced fraction

13. A bin contains 3 red and 4 green balls. 3 balls are chosen at random, with replacement. Let the random variable X be the number of green balls chosen. a. Explain why X is a binomial random variable. b. Construct a probability distribution table for X. c. Find the mean (expected value) of X. d. Use the law of Large Numbers to interpret the meaning of the expected value of X in the context of this problem.

Suppose you pick people at random and ask them what month of the year they were born in. Let X be the number of people you have to ask until you findnd a person who was born in December. (Just assume each month is equally likely to make it simpler.)

A) Find the probability that you had to ask exactly 9 people given that you had to ask at least 3 people. Ans: 0.04944

Calculate the value of the covariance between the stock and bond funds. Do not round intermediate calculations. Enter a decimal number rounded to 5 decimal places

Find the probabilities of getting the numbers from 1 to 6 upon rolling a die. Then find the probabilities of getting the numbers from 1 to 12 upon rolling two dice and summing the values that appear on their faces. Use technology to find and plot the corresponding probabilities for sums of 3, 4, 5, 10, 20, 50, and 100 dice. (a) As the number of dice increase, what shape does the probability distribution appear to approximate?

Two fair dice are tossed, and (X,Y) denote the number of spots on the first and on the second dice. Consider two random variables: U = X + Y and W = | X - Y |.

A). Derive the distribution of U. List all possible values and evaluate their probabilities.

B). Derive the distribution of W. List all possible values and evaluate their probabilities.

C). Determine the conditional probability P[6 <= U <= 7 | W <= 1]

The daily number of patients in the Emergency room is assumed to be normally distributed (bell shaped curve) with a mean of 200 and a standard deviation of 30.  Answers not showing work will receive no credit.  

7. What is the probability there will be more than 250 patients? Draw a sketch along with your answer.

8. 80% of the time the daily amount of patients will be between what 2 numbers? Draw a sketch along with your answer.

    9     Would 180 patients be an outlier?

A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the last​ century, the mean number of major hurricanes to strike a certain​ country's mainland per year was about 0.59 Find the probability that in a given year​ (a) exactly one major hurricane will strike the​ mainland, (b) at most one major hurricane will strike the​ mainland, and​ (c) more than one major hurricane will strike the mainland.

Let a bowl contain 15 chips of the same size and shape. Only one of those chips is red. Continue to draw chips from the bowl, one at a time at random and without replacement, until the red chip is drawn. Show your work.

a) Find the probability mass function of X, the number of trials needed to draw the red chip.

b) Compute the mean and variance of X.

c) Determine P(X <= 10).

Let X represent number of times someone went to a bagel store in one month. Assume that the following table is the probability distribution of X: a. What are the “expected value” and “standard deviation” of X?

X 0 1 2 3

P(X) 0.10 0.30 0.40 0.20

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Question: If I were to compute the conventional mean of X, my answer would be X=1.5. Why does the answer in (a) differ?