An 8-sided die has its faces numbered 2, 4, 6 16. What is the expected outcome on a typical roll?

The binomial and hypergeometric distributions are similar in that

A they both use independent trials

B they both use dependent trials

C they use the same formula for calculating the expectation

D they both involve counting successes

The expectation for a uniform distribution is calculated using

A. \displaystyle \frac{1}{n}\sum^{n}_{i=1}x_ki

B. \frac{ra}{n}

C. n p

D. \frac{x}{n}

Counting the number of tails when a coin is flipped 20 times is an example of a

A binomial distribution

B hypergeometric distribution

C uniform distribution

D none of the above

The probability that exactly two students will be selected when five people are selected from four students and three teachers is

A. \frac{2}{5}

B. \frac{_4C_2 \times _3C_3}{_7C_5}

C. \displaystyle _5C_2(\frac{4}{7})^2(\frac{3}{7})^3

D. \displaystyle \frac{5 \times 4}{7}

A particular traffic light is programmed to be red 40% of the time. On his daily Monday to Friday commute to and from work, what is the expected number of times Jack can expect to have a red light?

Three cards are selected, without replacement, from the honour cards (10, I, Q, K, A) in a standard deck. What is the probability that two of them are face cards?

a) Is the situation in modelled by a binomial or a hypergeometric distribution? Explain.

b) Describe how to change the situation to the binomial or hypergeometric distribution, as appropriate.

The beaver population in a particular provincial park is known to be 452. Two hundred beavers were caught and tagged. If 65 beavers were later caught and checked for tags, how many would you expect to be tagged?

Two dice are rolled a total of eight times, and the sum is recorded each time.

a) Show the probability distribution for a sum of 7.

b) Make a probability histogram of the distribution.

c) Determine and interpret the expected outcome.

A certain cell phone provider's help line is busy 95% of the time.

a) In 15 calls to the help line, what 1's the probability that it will be busy every time? at least 12 times?

b) What is the expected number of times a caller should expect the line to be busy in 15 attempts?

Ten males and five females applied for four job promotions. The union's affirmative action committee is concerned that no females were hired, saying that at least one should have been female. Use appropriate calculations to support or refute their claim.

The incidence of a disease in the population is 12%. Six people are in an elevator.

a) What is the probability that at least two of them will have the disease?

b) What is the expected number of these people with the disease?

Eighteen of thirty players selected in the NHL first—round draft were Canadian. lf seven drafted players are randomly selected, what is the probability that

a) only one is Canadian?

b) all are Canadian?

c) most of them are Canadian?

lf \frac{n}{4} > 200, the binomial distribution can be used to approximate the hypergeometric distribution. Why would this be?

Four numbers are chosen from six positive and eight negative numbers. What is the probability that the product of these four numbers will be positive, given that there is no repetition of numbers?