1. The BW company produces two models of products as shown here:
|
|
|
color
|
|
|
model
|
blue
|
brown
|
white
|
|
XB-50
|
445
|
105
|
330
|
|
YZ-99
|
40
|
402
|
75
|
a. Using relative frequency assessment, what is the probability that a manufactured item is brown?
b. What is the probability that the product manufactured is a YZ-99?
c. What is the joint probability that the product is a YZ-99 and brown?
2. Historically on Christmas Day the weather in Kansas has the following distribution pattern:
|
Event
|
Probability
|
|
Clear and Dry
|
0.4
|
|
Cloudy and Dry
|
0.1
|
|
Rain
|
0.3
|
|
Snow
|
0.2
|
a. What is the probability that next Christmas will be dry?
b. What is the probability that the next Christmas will be rainy or cloudy?
c. Given that the next Christmas is dry, determine the probability that it will also be cloudy.
3. A basketball team has 10 players: 5 are seniors, 2 are juniors, and 3 are sophomores. 2 players are randomly selected to serve as captains for each game. What is the probability that both players selected are juniors?
4. Given the following contingency table what is the probability of
a. Event A occurring
b. Event A and B occurring
5. Which of the following events occur with a probability of 0?
a. A voter in the US is registered as a Democrat and a Republican
b. A voter in the US is a minority and registered as a Republican
c. An automobile is both a Ford and a Chevy
d. An automobile that is a BMW is produced in the United States
6. What is the difference between mutually exclusive and collectively exhaustive events?
7. Using this sample data and relative frequency, what is the probability that an employee has 0 vacation days left?
|
13
|
0
|
2
|
0
|
1
|
3
|
5
|
2
|
|
5
|
1
|
3
|
0
|
0
|
1
|
3
|
3
|
|
4
|
3
|
1
|
28
|
14
|
2
|
4
|
0
|
8. Using relative frequency, what is the probability of a sample data coming back as at least 1022?
|
2
|
339
|
650
|
864
|
1025
|
1261
|
1535
|
|
16
|
340
|
655
|
883
|
1028
|
1280
|
1538
|
|
88
|
395
|
669
|
883
|
1036
|
1290
|
1648
|
|
96
|
457
|
703
|
890
|
1044
|
1312
|
1653
|
|
103
|
478
|
730
|
934
|
1087
|
1341
|
1770
|
|
115
|
501
|
763
|
951
|
1091
|
1355
|
1799
|
|
124
|
521
|
788
|
969
|
1126
|
1357
|
1838
|
|
148
|
556
|
789
|
985
|
1176
|
1360
|
1864
|
|
164
|
583
|
789
|
993
|
1199
|
1414
|
1920
|
|
212
|
595
|
802
|
997
|
1199
|
1436
|
1965
|
|
265
|
596
|
822
|
999
|
1237
|
1479
|
1972
|
|
288
|
604
|
851
|
1018
|
1242
|
1492
|
2032
|
Using the table above and cumulative frequency, what is the probability that the sample will be less than 257?