Problem #1:

(a)	From a stack of 3 dice, one is taken and rolled twice. If, unknown to the gambler, one of the dice is weighted and has a 1/8 chance of rolling a 6, what is the probability that the gambler rolls two 6's?

(b)	If the gambler has rolled two sixes, what is the probability that he has rolled the weighted die?

Problem #2:

Many students entering unversity take a math course, 1J03. In this course, 7% of the students fail, and leave the university. 26% of the students pass, but get a low mark, and move on to 1E03. 67% of the students pass, and get a high mark, and move on to 1KR3. In 1E03, 15% fail, and leave the university. In 1KR3, 17% fail, and depart. If a student tells his parents he failed mathematics and had to leave the university, what is the probability that he failed out of 1E03?

Problem #3:

A production manager counts the number of items produced in his factory in a given 40 hour week. He records the following data:

# Produced Per Hour	Number of Occurrences	Relative Frequency
51 52 53 54 55 56	3 7 6 19 11 4	a b c d e f

The third column in the above table contains the frequencies for arelativefrequency distribution associated with this data. Find the values ofa,b,c,d,e, and f.

Enter the values ofa,b,c,d,e,f in that order, separated by commmas.

Problem #4:

The random variableYhas the following probability distribution.

k	Pr(Y=k)
3 6 9 12 15	0.2 0.22 0.3 0.09 0.19

The random variable (3 - (Y/3))²has a probability distribution of the following form.

k	Pr((3 - (Y/3))2=k)
a b c	d e f

where the values ofa,b, andc, are inincreasingorder.

(a)	Find the values ofa,b, andc.

(b)	Find the values ofd,e, and f.

.

Problem #5:

38% of all pets sold at a pet store are dogs. One day, 12 people arrive at the store and purchase pets. (Note: One pet is purchased per person.)

(a)	What is the probability that exactly 5 of them are dogs?

(b)	If the store has only 10 dogs, what is the probability that they have sufficient dogs for sale that day?

Problem #6:

A single die is rolled 5 times. What is the probability that a six is rolled exactly once, if it is known that at least one six is rolled?

Problem #7:

A die is rolled 30 times, and the value on top of the die recorded. This produces the following results:

Value	# Occurences
1 2 3 4 5 6	8 3 2 4 3 10

(a)	For this data, compute the mean value on the die in this experiment.

(b)	Now, compute the expected value for this experiment.

Round your answer to2 decimals.

Problem #8:

A carnival operator is constructing a new game. In this game, the player will place a bet. Then a ball is selecteded from an urn containing balls of three colours: 1 green ball, 5 red balls and 5 white balls. If a red ball is drawn, the player wins 3$, if a green ball is drawn, the player wins 4$, and if a white ball is drawn the player wins nothing. What should the carnival operator set the bet at such that on average he makes $0.50 profit a game? (That is, so the player loses $0.50)

Problem #9:

Suppose we are given a probability distribution that has a mean if 10 and a standard deviation of 0.9. Use the Chebyshev inequality to find a lower bound estimate of the following probabilities:

(a)	The probability that the outcome will lie between 8 and 12

(b)	The probability that the outcome lies between 4.5 to 15.5

Problem #10:

What is the probability that a normal random variable has an outcome within 3 standard deviations of the mean?

Problem #11:

In her first year of university, Mary recieved the following grades: 7, 10, 12, 6, 11, 6 Similarly in his first year, Bob recieved the following grades: 11, 10, 7, 11, 6, 11

(a)	Compute the population mean and variance for Mary's grades.

(b)	Compute the population mean and variance for Bob's grades.

Problem #12:

Suppose that Student A's marks throughout the term had a mean of 90 with variance 9, and that Student B's marks throughout the term had a mean of 70 with variance 36. Which of the below statements is true?

(A)Neither student had a higher average and neither student was more consistent. (B)Neither student had a higher average and Student A was more consistent. (C)Student A had a higher average but neither student was more consistent. (D)Student A had a lower average but neither student was more consistent. (E)Student A had a lower average and was more consistent. (F)Student A had a higher average and Student B was more consistent. (G)Neither student had a higher average and Student B was more consistent. (H)Student A had a higher average and was more consistent. (I)Student A had a lower average and Student B was more consistent. Problem #12:

SelectABCDEFGHI

Problem #13:

For the standard normal distribution, determine the following probabilities:

(a)	Pr(Z 1.35)

(b)	Pr(1.5 Z 2.4)

Give your answer to4 decimals.

Problem #14:

For a normal random variable, with = 19, and = 10, find the following probabilities.

(a)	Pr(X 23.5)

(b)	Pr(X> 4.00)

Problem #15:

A very reliable baseball player is known to get a hit when at bat 41% of the time. He is expected to have 107 more times at bat before the end of the season, and he is 50 hits away from breaking a league hitting record. What is the probability of him breaking that record before the end of the season?

Problem #16:

A child, (and mathematical genius!) wishes to estimate the variability in the number of candies he can collect from houses during trick-or-treating. He randomly selects asampleof 20 houses, and records the number of candies he gets at each:

# Candies	# Houses
0 1 2 3 4	1 8 5 3 3

Find the sample variance he calculates using this data.