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Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 3: 1 (page 167)

An experiment results in one of the following sample points: $E_{1}, E_{2}, E_{3}$ or $E_{4}$ . Find $P (E_{4})$ for each of the following cases.
$P (E_{1}) = 0.1, P (E_{2}) = 0.2, P (E_{3}) = 0.3$
$P (E_{1}) = P (E_{2}) = P (E_{3}) = P (E_{4})$
$P (E_{1}) = P (E_{2}) = 0.1$ and $P (E_{3}) = P (E_{4})$

Short Answer

Expert verified

$P (E_{4}) = 0.4$
$P (E_{4}) = 0.25$
$P (E_{4}) = 0.4$

Step by step solution

01

Finding the Probability of the event E4 where PE1=0.1,PE2=0.2,PE3=0.3

The probability of all the sample points within a sample space is equal to $鈭� Pi = 1$

Given $P (E_{1}) = 0.1, P (E_{2}) = 0.2, P (E_{3}) = 0.3$

$P (E_{1}) + P (E_{2}) + P (E_{3}) + P (E_{4}) = 1 0.1 + 0.2 + 0.3 + P (E_{4}) = 1 P (E_{4}) = 1 - (0.1 + 0.2 + 0.3) P (E_{4}) = 0.4$

The probability of observing the event $E_{4}$ is 0.4.

02

Finding the probability of the event E4 where PE1 = PE2 = PE3 = PE4

The probability of all the sample points within a sample space is equal to $鈭� Pi = 1$ .

Given,

$P (E_{1}) = P (E_{2}) = P (E_{3}) = P (E_{4})$

$P (E_{1}) + P (E_{2}) + P (E_{3}) + P (E_{4}) = 1 4 脳 P (E_{4}) = 1 P (E_{4}) = \frac{1}{4} P (E_{4}) = 0.25$

The probability of observing event $E_{4}$ is $0.25$ .

03

Finding the probability of the event E4 where PE1=PE2=0.1 and PE3=PE4

The probability of all the sample points within a sample space is equal to $鈭� Pi = 1$ .

Given,

$P (E_{1}) = P (E_{2}) = 0.1$ and $P (E_{3}) = P (E_{4})$

$P (E_{1}) + P (E_{2}) + P (E_{4}) = 1 0.1 + 0.1 + 2 脳 P (E_{4}) = 1 2 脳 P (E_{4}) = 1 - (0.1 + 0.1) P (E_{4}) = 0.4$

The probability of observing the event $E_{4}$ is 0.4 .

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Most popular questions from this chapter

The diagram below describes the sample space of a particular experiment and events A and B .

What is this type of diagram called?
Suppose the sample points are equally likely. Find $P (A)$ and $P (B)$ .
Suppose $P (1) = P (2) = P (3) = P (4) = \frac{1}{16}$ and $P (5) = P (6) = P (7) = P (8) = P (9) = P (10) = \frac{1}{8}$ . Find $P (A)$ and $P (B)$ .

鈥淟et鈥檚 Make a Deal.鈥滿arilyn vos Savant, who is listedin Guinness Book of World Records Hall of Fame for鈥淗ighest IQ,鈥� writes a weekly column in the Sunday newspaper supplement Parade Magazine. Her column, 鈥淎skMarilyn,鈥� is devoted to games of skill, puzzles, and mind-bendingriddles. In one issue (Parade Magazine, February 24, 1991), vos Savant posed the following question:

Suppose you鈥檙e on a game show, and you鈥檙e given a choice of three doors. Behind one door is a car; behind the others, goats. You pick a door鈥攕ay, #1鈥攁nd the host, who knows what鈥檚 behind the doors, opens another door鈥攕ay #3鈥攚hich has a goat. He then says to you, 鈥淒o you want to pick door #2?鈥� Is it to your advantage to switch your choice?

Marilyn鈥檚 answer: 鈥淵es, you should switch. The first door has a 13 chance of winning [the car], but the second has a 23 chance [of winning the car].鈥� Predictably, vos Savant鈥檚 surprising answer elicited thousands of criticalletters, many of them from PhD mathematicians, who disagreed with her. Who is correct, the PhDs or Marilyn?

Simulate the experiment described in Exercise 3.7 using any five identically shaped objects, two of which are one colour and the three another colour. Mix the objects, draw two, record the results, and then replace the objects. Repeat the experiment a large number of times (at least 100). Calculate the proportion of time events A, B, and C occur. How do these proportions compare with the probabilities you calculated in Exercise 3.7? Should these proportions equal the probabilities? Explain.

Investing in stocks. From a list of 15 preferred stocks recommended by your broker, you will select three to invest in. How many different ways can you select the three stocks from the 15 recommended stocks?

Study of why EMS workers leave the job.Refer to the Journal of Allied Health(Fall 2011) study of why emergencymedical service (EMS) workers leave the profession,Exercise 3.45 (p. 182). Recall that in a sample of 244former EMS workers, 127 were fully compensated whileon the job, 45 were partially compensated, and 72 hadnon-compensated volunteer positions. Also, the numbersof EMS workers who left because of retirement were 7 forfully compensated workers, 11 for partially compensatedworkers, and 10 for no compensated volunteers.

a.Given that the former EMS worker was fully compensatedwhile on the job, estimate the probability that theworker left the EMS profession due to retirement.

b.Given that the former EMS worker had a non-compensatedvolunteer position, estimate the probabilitythat the worker left the EMS profession due toretirement.

c.Are the events {a former EMS worker was fully compensatedon the job} and {a former EMS worker left thejob due to retirement} independent? Explain.

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