Exam 5: Probability: Review of Basic Concepts

Dormitory A dormitory has two activating devices in each fire detector.One is smoke activated and has a probability of .98 of sounding an alarm when it should.The second is a heat sensitive activator and has a probability of .95 of operating when it should.Each activator operates independently of the other.Presume a fire starts near a detector. -What is the probability that only the smoke activator functions?

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. -Are the events C and F independent?

Shoe store A shoe store carries 590 pairs of Stacy-Adams and 610 pairs of Freeman brands of shoes.Let a success be the event of randomly selecting a pair of Stacy-Adams shoes. Find the probability of a success.

You have applied for a job and are told by the interviewer that the probability of your being hired is 0.70.Calculate the odds that you will be hired. The odds are ____________________ to ____________________.

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).

If inspection finds the item to be defective,what is the revised probability that the item came from machine 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. -An investment counselor would like to meet with 14 of his clients on Wednesday,but he only has time for 10 appointments.How many different combinations of the clients could be considered for inclusion into his limited schedule for that day?

Manufacturers A large men's store in a mall purchases suits from four different manufacturers in short,regular,and long.Their current selections are given in the contingency table below: Маnufacturers Length Total S 15 15 35 35 100 R 60 70 75 70 275 L 25 35 40 25 125 Total: 100 120 150 130 500 Let the abbreviations and letters represent the events.For example Event S = a randomly selected suit is short,event HMS = a randomly selected suit is manufactured by HMS. -Compute P(S /HMS).

If the probability of drawing an Ace from a deck of cards is 0.077 and the probability of rolling a "2" using a fair die is 0.167,then the probability of drawing an Ace and rolling a "2" is

Shoe store A shoe store carries 590 pairs of Stacy-Adams and 610 pairs of Freeman brands of shoes.Let a success be the event of randomly selecting a pair of Stacy-Adams shoes. Find the odds of selecting a pair of Stacy-Adams shoes. The odds are ____________________ to ____________________.

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 /D)is equal to:

If the probability of an event is x,with $0 \leq x \leq 1$ ,then the odds in favor of the event are x to (1 - x).

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 -Is the sale of Mother Burgers independent of profitability of store?

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 no checking account and no savings account is:

According to an old song lyric,"love and marriage go together like a horse and carriage." Let love be event A and marriage be event B.Are events A and B mutually exclusive?

A Gulf Coast travel park has the following accommodations: Number of Gedrams Location 3 Gedranm 4 Gedranm Tatal Beach Frant 17 24 41 Nan Beach Frant 6 210 216 Tatal 23 234 257 Is the event of selecting a beach front site independent of the event of selecting a 3 bedroom facility? Explain.

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(E / B).

The relative frequency approach to probability depends on the law of ______________________________.

Odds The odds in favor of an event are the number of successes divided by the number of failures.The probability of this event occurring is the number of successes divided by the sum of the number of successes and the number of failures.The number of successes is five and the number of failures is four. Find the odds in favor of success. The odds are ____________________ to ____________________.

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. -A study of Brand D washing machines that failed within three years (warranty period)was 23.2%.Of those that failed,82.9% lasted over two years.What is the probability that a washer,which lasts at least two years,will still fail before the end of the warranty period?