Exam 5: Probability: Review of Basic Concepts

Probabilities The prior probabilities for two events A₁ and A₂ are P(A₁)= .30 and P(A₂)= .70.It is also known that P(A₁ and A₂)= 0.Suppose P(B / A₁)= .15 and P(B / A₂)= .05. Are A₁ and A₂ mutually exclusive? Explain.

College The table below indicates the number of majors found in a college of business: -What is the probability that a randomly selected student is a finance major and an accounting major?

Interest rates The following represent interest rates on 20 U.S.Treasury bond issues with maturity dates in 2000-2001,as listed in Money Magazine: -Determine the probability that a randomly selected bond will have a rate of interest of 11 percent or more.

Probability refers to a number between ____________________ and ____________________ which expresses the ____________________ that an event will occur.

Basketball Team A basketball team at a university is composed of ten players.The team is made up of players who play either guard,forward,or center position.Four of the ten are guards; four of the ten are forwards; and two of the ten are centers.The numbers of the players are 1,2,3,4,for the guards; 5,6,7,8 for the forwards; and 9 and 10 for the centers.The starting five are numbered 1,3,5,7,and 9.Let a player be selected at random from the ten.Define the following events: A = player selected has a number from 1 to 8. B = player selected is a guard. C = player selected is a forward. D = player selected is a starter. E = player selected is a center. -P(B and D)is equal to:

In general,an event is one of the possible outcomes of an experiment.

Sometimes it is useful to revise a probability on the basis of additional information that we didn't have before.

Burger Queen Co. The Burger Queen Company has 124 locations along the west coast.The general manager is concerned with the profitability of the locations compared with major menu items sold.The information below shows the number of each menu item selected by profitability of store. Profit Baby Burger MI Mother Burger Father Burger Nachos M4 Tacos Total High Profit RI 250 424 669 342 284 1969 Medium Profit R2 312 369 428 271 200 1580 Low Profit R3 289 242 216 221 238 1206 Total: 851 1035 1313 834 722 4755 -What is the probability of selecting a menu item from a high profit store and it is nachos?

Portfolio Composition An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds,primarily stocks,or a balanced mix of bonds and stocks).The proportions of clients falling into the various categories are shown in the following table: Partfolin Compasition Cender Ennds Stacks Galanced Mala 0.18 0.20 0.25 Female 0.12 0.05 0.20 One client is selected at random,and two events A and B are defined as follows: A: The client selected is male. B: The client selected has a balanced portfolio. -Find the following probabilities: A)P(A/B) B)P(B/A)

Define conditional probability.

Appliance dealer An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period.The records were: No. of service calls Relative frequency 0 0.25 1 0.38 2 0.30 3 0.04 4 0.03 -Let X be the number of service calls during the warranty period for a dishwasher.What is the probability that there will be exactly one service call?

Which of the following is not an approach to assigning probabilities?

Uncertainty plays an important role in our daily lives and activities as well as in business.

Explain why events C and F are or are not independent.

An event A and its complement A' are always ___________________________________.

Appliance dealer An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period.The records were: No. of service calls Relative frequency 0 0.25 1 0.38 2 0.30 3 0.04 4 0.03 -Let X be the number of service calls during the warranty period for a dishwasher.What is the probability that there will be between two and four (inclusive)service calls?

When events are ____________________ the occurrence of one means that none of the others can occur.

Plan to buy Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below: Plan to buy Qualify for Financing Within 6 months () 6 months or longer () No (C) Yes (D) 0.30 0.20 0.10 No (E) 0.10 0.10 0.20 -For a randomly selected consumer,find the following probability: P(D).

Define contingency table.

A survey revealed that 21.5% of the households had no checking account,66.9% had regular checking accounts,and 11.6% had NOW accounts.Of those households with no checking account 40% had savings accounts.Of the households with regular checking accounts 71.6% had a savings account.Of the households with NOW accounts 79.3% had savings accounts. The probability that a randomly selected household has a savings account is: