Exam 5: Probability: Review of Basic Concepts

Telephone survey A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law.Each person was identified as either Republican or Democrat.The results are shown in the following table: Party In Favar Nat in Favar Undecided Tatal Republican 98 54 4\square 192 Democrat 79 29 60 168 Tatal 177 83 100 360 -Given that the respondent was in favor of the proposed law,what is the probability that they were a Republican?

Event Event Event Total DI 75 125 65 35 300 D2 90 105 60 45 300 D3 135 120 75 70 400 Total: 300 325 200 150 1000 -Find P (C1 and D1).

When we wish to determine the probability that one or more of several events will occur in an experiment,we would use ____________________ rules.

If A and B are independent events with P(A)= 0.25 and P(B)= 0.60,then P(A/B)is:

Event 1 The prior probabilities of events A₁,A₂,and A₃ are P(A₁)= .50,P(A₂)= .20 and P(A₃)= .30.The conditional probabilities of event B given A₁,A₂,and A₃ are P(B / A₁)= .40,P(B / A₂)= .50 and P(B / A₃)= .30. -Apply Bayes' theorem to compute the posterior probability P(A₃ / B).

Event 1 The prior probabilities of events A₁,A₂,and A₃ are P(A₁)= .50,P(A₂)= .20 and P(A₃)= .30.The conditional probabilities of event B given A₁,A₂,and A₃ are P(B / A₁)= .40,P(B / A₂)= .50 and P(B / A₃)= .30. -Compute P(B and A₂).

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(A)is equal to:

Candidate Six candidates for a new position of vice-president for academic affairs have been selected.Three of the candidates are female.The candidates' years of experience are as follows: Candidate Experience Female 1 5 Female 2 9 Female 3 11 Male 1 6 Male 2 4 Male 3 8 Suppose one of the candidates is selected at random.Define the following events: A = person selected has 9 years experience. B = person selected is a female. -Find P(not A / B).

Create a Venn diagram illustrating an Event A,and its complement.

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)is equal to:

Prior probability is a marginal probability while posterior probability is a conditional probability.

The odds of the Dallas Cowboys winning this year's Super Bowl are 3 to 1.Compute the probability of the Cowboys winning.

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. -Compute P(A₁ and B).

The relative frequency approach to probability is judgmental,representing the degree to which one happens to believe that an event will or will not happen.

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. -Apply Bayes' theorem to compute P(A₁ / B).

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 at least 14 percent,but less than 15 percent.

I would like to select 3 paperback books from a list of 12 books to take on vacation.How many different sets of 3 books can I choose?

An experiment is an activity of measurement that results in an outcome.

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 item was selected the least at any type store? What percentage of the time was this item selected?

Gender The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows: Gender Major Male Female Total Physics 25 25 50 Chemistry 60 40 100 Geology 30 20 50 Total 115 85 200 Suppose a person is selected at random from these graduates.Consider the following events: M: The person is a male. F: The person is a female. P: The person graduated in physics. C: The person graduated in chemistry. G: The person graduated in geology. -Find P(M / P).