Can you please do #6 part c and #8 part c Can you please do #6 part c and #8 par

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Can you please do #6 part c and #8 part c

Can you please do #6 part c and #8 part c

QUESTION6 Nine balls numbered 1 through 9 are placed in a bowl, and 5 are selected without replacement. (a) Find the probability that the ball with the largest number selected is 7. (b) Find the probability that the ball with the largest number selected is 7 and the one with the smallest number selected is 2 (c) Denote the range of numbers on selected balls as R Largest Number - Smallest Number Therefore, in (b), R-7-2-5. Bearing in mind that this is not the only combination of numbers that could produce R-5, find the probability that the range of numbers on selected balls is 5? d) Give all possible values for R and find the probabilities associated with these values. UESTION 7 A certain multinational corporation employs a large number of people from all over the world. It is known that 54% of all people employed by this corporation are from Canada. In addition, 22% of all employees hold management positions. Ofall Canadian employees, 31% hold management positions. (a) What is the probability that a randomly selected employee is (1) Canadian and holds a management position, (2) Canadian or holds a management position, or both? (b) What proportion of those holding management positions are Canadian? (c) What proportion of all employees hold a management position but are not Canadian? (d) Is the event that a randomly selected employee is Canadian independent of the event that a randomly selected employee holds a management position? Explain. (e) Refer to (d). Are these two events mutually exclusive? Explain. An automobile insurance company classifies each driver as a good risk, a medium risk, or a bad risk. Of those currently insured, 30% are good risks, 50% are medium risks, and 20% are bad risks. In any given year, the probability of at least one citation is 0.1 for a good-risk driver, 0.3 for a medium-risk driver, and 0.5 for a bad-risk driver (a) What proportion of drivers receive a citation during a particular year (b) If a randomly selected driver is found to have at least one citation in a particular year, what is the probability that the driver is a good risk? (c) If a randomly selected driver is found to have no citations in a particular year, what is the probability that the driver is a bad risk?

Explanation / Answer

6.c. Since 5 are selected without replacement, the maximum values can be 9,8,7,6,5.

Minimum values can be 1,2,3,4,5.

All possible subtractions are

8 = 9-1

7 = 9-2, 8-1

6 = 9-3, 8-2, 7-1

5 = 9-4, 8-3, 7-2, 6-1

4 = 9-5, 8-4, 7-3, 6-2, 5-1

3 = 9-6, 8-5, 7-4, 6-3, 5-2

2 = 9-7, 8-6, 7-5, 6-4, 5-3

1 = 9-8, 8-7, 7-6, 6-5, 5-4

Altogether there are 30 values.

Possible different values of R and their probabilities are:

8 : 1/30 = 0.033

7 : 2/30 = 0.066

6: 3/30 = 0.1

5: 4/30 = 0.133

4: 5/30 = 0.166

3: 5/30 = 0.166

2: 5/30 = 0.166

1: 5/30 = 0.166

8.c. Probability that a good risk driver has no citations = 1 - 0.1 = 0.9

=> Probability that a driver is a good risk driver with no citations = 0.9 * 0.3 = 0.27

Probability that a medium risk driver has no citations = 1 - 0.3 = 0.7

=> Probability that a driver is a medium risk driver with no citations = 0.7 * 0.5 = 0.35

Probability that a bad risk driver has no citations = 1 - 0.5 = 0.5

=> Probability that a driver is a bad risk driver with no citations = 0.5 * 0.2 = 0.1

Therefore probability that a driver with no citations is a bad risk driver = 0.1 / (0.27 + 0.35 + 0.1)

= 0.139

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