Which events are independent?Use your intuitive understanding of independence to form an opinion about whether each of the following scenarios represents independent events.

a.The results of consecutive tosses of a coin.

b.The opinions of randomly selected individuals in a pre-election poll.

c.A Major League Baseball player's results in two consecutive at-bats.

d.The amount of gain or loss associated with investments in different stocks if these stocks are bought on the same day and sold on the same day 1 month later.

e.The amount of gain or loss associated with investments in different stocks bought and sold in different time periods, 5 years apart.

f.The prices bid by two different development firms in response to a building construction proposal.

Short Answer

Expert verified
  1. Event A is independent.
  2. Event B is independent.
  3. Event C is independent.
  4. Event D is not independent.
  5. Event E is independent.
  6. The event F is not independent.

Step by step solution

01

(a) The results of consecutive tosses of a coin

To the data, some flip of a coin does not produce another flip of a coin event. So, event A is independent.

02

(b) The opinions of randomly selected individuals in a pre-election poll

Based on the facts, the view of a randomly picked person together in a pre-election study probably does not impact someone person's current view. Hence, event B is independent.

03

(c) A Major League Baseball player's results in two consecutive at-bats

A. To data, the result of such discussion does not affect something else's occurrence. Accordingly, event C is independent.

04

(d) The amount of gain or loss associated with investments in different stocks if these stocks are bought on the same day and sold on the same day 1 month later

A. To data because of this the earnings or losses in respect of investments in various equities purchased the same day. They offered one month ago and are expected to be substantially connected. Hence, event D is not independent.

05

(e) The amount of gain or loss associated with investments in different stocks that are bought and sold in different time periods, 5 years apart

A. To the data, because occurrences eventuate 5 years separately that is improbable that some stock's bought and sold will influence the purchase and offer from another firm. So, event E is independent.

06

(f) The prices bid by two different development firms in response to a building construction proposal

Since each developer as the data cannot decide the proposition. So, the event F is not independent. Therefore, event F is not independent.

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Most popular questions from this chapter

Reliability of gas station air gauges. Tire and automobile manufacturers and consumer safety experts all recommend that drivers maintain proper tire pressure in their cars. Consequently, many gas stations now provide air pumps and air gauges for their customers. In a Research Note(Nov. 2001), the National Highway Traffic Safety Administration studied the reliability of gas station air gauges. The next table gives the percentage of gas stations that provide air gauges that over-report the pressure level in the tire.

a. If the gas station air pressure gauge reads 35 psi, what is the probability that the pressure is over-reported by 6 psi or more?

b. If the gas station air pressure gauge reads 55 psi, what is the probability that the pressure is over-reported by 8 psi or more?

c. If the gas station air pressure gauge reads 25 psi, what is the probability that the pressure is not over-reported by 4 psi or more?

d. Are the events A= {over report by 4 psi or more} and B= {over report by 6 psi or more} mutually exclusive?

e.Based on your answer to part d, why do the probabilities in the table not sum to 1?

Suppose the events B1and B2are mutually exclusive and complementary events, such thatP(B1)=.75andP(B2)=.25 Consider another event A such that role="math" localid="1658212959871" P(AB1)=.3, role="math" localid="1658213029408" P(AB2)=.5.

  1. FindP(B1A).
  2. FindP(B2A)
  3. Find P(A) using part a and b.
  4. Findrole="math" localid="1658213127512" P(B1A).
  5. Findrole="math" localid="1658213164846" P(B2A).

In a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. One of the 106 social robots is randomly selected and the design (e.g., wheels only) is noted.

  1. List the sample points for this study.
  2. Assign reasonable probabilities to the sample points.
  3. What is the probability that the selected robot is designed with wheels?
  4. What is the probability that the selected robot is designed with legs?

Wine quality and soil.The Journal of Wine Research(Vol.21, 2010) published a study of the effects of soil and climate on the quality of wine produced in Spain. The soil at two vineyards— Llarga and Solar—was the focus of the analysis.Wine produced from grapes grown in each of the two vineyards

was evaluated for each of three different years (growing seasons) by a wine-tasting panel. Based on the taste tests, the panel (as a group) selected the wine with the highest quality.

a.How many different wines were evaluated by the panel, where one wine was produced for each vineyard/growing season combination?

b.If the wines were all of equal quality, what is the probability that the panel selected a Llarga wine as the wine with the highest quality?

c.If the wines were all of equal quality, what is the probability that the panel selected a wine produced in year 3 as the wine with the highest quality?

d.The panel consisted of four different wine tasters who performed the evaluations independently of each other. If the wines were all of equal quality, what is the probability that all four tasters selected a Llarga wine as the wine with the highest quality?

For two events, A and B, P(A)=.4 , P(B)= .2, and P(A/B)= .6:

a. Find P (AB).

b. Find P(B/A).

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