Practice Probability and Statistics Questions

Question 1: Calculate the following probabilities and SHOW your calculations:

(a) Probability that a card chosen at random from a standard deck of cards will be either a face card or a non-face card with an odd number?

(b) The probability to roll an odd number or a number less than 9, using two dice in a single roll.

Question 2: Muddy’s at Convenience Store at downtown Wolfville has been the target of many shoplifters during the past month, but 125 shoplifters have been caught thanks to the hidden security cameras in the store. RCMP released the tabulations regarding a shoplifter’s sex (male vs female) and his/her criminal history (first-time vs repeat offender). The data are summarized in the table. Use the table to answer the questions and SHOW your CALCULATIONS FOR EACH PART.

 (a) What is the probability that a randomly chosen shoplifter is a female?
(b) What is the probability that a randomly chosen shoplifter is a repeat offender?
 (c) What is the probability that a randomly chosen shoplifter is a female and a repeat offender?
 (d) What is the probability that a randomly chosen shoplifter is a repeat offender or a female
  (e) What is the probability that a randomly chosen repeat offender is a female?
 (f) What is the probability a shoplifter is a repeat offender given that she is a female?(g) Are the events, criminal history and sex of the shoplifter, statistically independent of each other? Explain.
Question 3: Suppose that you are trying to develop a strategy for investing in a portfolio that consists of two different stocks (stock X and stock Y). The anticipated annual return for $1000 investment in each stock under four different economic conditions has the following probability distribution
(a) Compute the individual expected returns for stock X and stock Y.
(b) Compute the individual standard deviations for stock X and stock Y
(b) Compute the covariance between stock X and stock Y. Explain your result.
 (d) If you were to invest in either stock X or stock Y, which one would you prefer? Explai
(e) Suppose that now you want to create a portfolio that consists of stock X and stock Y. In particular, you want to have 40% of your portfolio consist of stock X and the remainder of your portfolio with stock Y. Compute the expected return on the portfolio and the portfolio risk (i.e. standard deviation of the return from the portfolio). Explain how these numbers compare to (as a % of) the risk and the return obtained when ONLY invested in stock X or Y? WITHOUT making calculations, explain how the expected return on the portfolio would change if we invested in both stocks X and Y equally.
 Question 4: Answer the following questions and show your calculations.
(a) A toll free phone number is available from 9 AM to 9PM for customer complaints about a product purchased from your company. Past history indicates that an average of 0.8 calls is received per minute. Calculate the probability that at most 2 calls will be received in a given minute?

 

(b) Suppose that you decided to go to Casino Nova Scotia for your birthday. Feeling especially lucky tonight, you sit on a blackjack table. You know that in a 52-card deck, there are 16 cards in total that a point value of 10 (tens and face cards of each suit). Moreover, there are 4 aces in a deck (one for each suit). The dealer gives you two cards. Calculate the probability that one of the cards in your hand is a 10-point card.

Question 5: You are the manager of the local Burger King branch in your town. You know that 89.7% of the orders in Burger are filled correctly in a given year. You just received 10 orders from various customers.  
 (a) What is the probability that none of these orders (i.e. 10) will be filled correctly?
(b) What is the probability that all of these orders (i.e. 10) will be filled correctly
(c) What is the probability that at most 7 of these orders will be filled correctlon