Chapter 3: Q99SE (page 203)
Given that and, findlocalid="1662699184645" .
The value of P(B) is 0.5.
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Degrees of best-paid CEOs.Refer to the results of the Glassdoor Economic Research (August 25, 2015) survey of the top 40 best-paid CEOs shown in Table 2.1 (p. 65). The data on the highest degree obtained are summarized in the SPSS printout below. Suppose you randomly select five of the CEOs (without replacement) and record the highest degree obtained by each.
a.What is the probability that the highest degree obtained by the first CEO you select is a bachelor’s degree?
b.Suppose the highest degree obtained by each of the first four CEOs you select is a bachelor’s degree. What is the probability that the highest degree obtained
by the fifth CEO you select is a bachelor’s degree?
USDA chicken inspection. The U.S. Department of Agriculture (USDA) reports that one in every 100 slaughtered chickens passes inspection with fecal contamination under its standard inspection system.
a. If a slaughtered chicken is selected at random, what is the probability of passing inspection with fecal contamination?
b. The probability of part a was based on a USDA study that found that 306 of 32,075 chicken carcasses passed inspection with fecal contamination. Do you agree with the USDA's statement about the likelihood of a slaughtered chicken passing inspection with fecal contamination?
Jamming attacks on wireless networks. Refer to the International Journal of Production Economics (Vol. 172, 2016) study of U.S. military jamming attacks on wireless networks used by terrorists, Exercise 2.8 (p. 73). Recall that 80 recent jamming attacks were classified according to network type (WLAN, WSN, or AHN) attacked and the network's number of channels (single- or multi-channel). The results are reproduced in the accompanying table.
a. Find the probability that a recent jamming attack involved a single-channel network.
b. Find the probability that a recent jamming attack involved a WLAN network.
Network Type/Number of Channels | Number of Jamming Attacks |
WLAN / Single | 31 |
WSN / Single | 13 |
AHN / Single | 8 |
WLAN / Multi | 14 |
WSN / Multi | 9 |
AHN / Multi | 5 |
TOTAL | 80 |
Source: S. Vadlamani et al., "Jamming Attacks on Wireless Networks: A Taxonomic Survey, "International Journal of Production Economics, Vol. 172, 2016 (Figure 6)
Problems at major companies. The Organization Development Journal (Summer 2006) reported on a survey of human resource officers (HROs) at major employers. The focus of the study was employee behaviour, namely, absenteeism and turnover. The study found that 55% of the HROs had problems with employee absenteeism; 41% had problems with turnover. Suppose that 22% of the HROs had problems with both absenteeism and turnover. Use this information to find the probability that an HRO selected from the group surveyed had problems with either employee absenteeism or employee turnover.
Chance of winning at “craps.” A version of the dice game“craps” is played in the following manner. A player starts by rolling two balanced dice. If the roll (the sum of the two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or a 3 (called craps), the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs
(in which case the player loses).
a. What is the probability that a player wins the game on the first roll of the dice?
b. What is the probability that a player loses the game on the first roll of the dice?
c. If the player throws a total of 4 on the first roll, what is the probability that the game ends (win or lose) on the next roll?
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