Amos, Bertie, and Chloe are servers for Damon's Dinner Dive. Amos serves 40% of the customers and receives complaints from 3% of his customers. Bertie serves 35% of the customers and receives complaints from 4% of her customers. Chloe serves 25% of the customers and receives complaints from 6% of her customers.

14. Label the tree diagram appropriately.

15. Complete the joint probability distribution.

Yes | No | Total | |
---|---|---|---|

Amos | 0.012 | 0.388 | 0.400 |

Bertie | 0.014 | 0.336 | 0.350 |

Chloe | 0.015 | 0.235 | 0.250 |

Total | 0.041 | 0.959 | 1.000 |

16. What percent of the customers complain about a server? 0.041 = 4.1%

17. A customer complains about a server. What is the probability the server was Chloe? 0.015 / 0.041 = 0.3659

A bag of candy has the following flavor distribution. 20% grape, 40% orange, and 30% cherry. The rest are lemon flavored. Assume that the bag has enough candy in it that the distribution is not affected by sampling without replacement.

18. Create a probability distribution for the flavor of candy.

Flavor | Grape | Orange | Cherry | Lemon | Total |
---|---|---|---|---|---|

Probability | 0.2 | 0.4 | 0.3 | 0.1 | 1.0 |

19. A single candy is randomly selected from the bag.

19a. What is the probability that it is lemon? 0.1

19b. What is the probability that it is grape or orange? 0.2 + 0.4 = 0.6

19c. What is the probability that it is not cherry? 1 - 0.3 = 0.7

20. Three candies are randomly selected from the bag.

20a. What is the probability that all three are grape? P(GGG) = 0.2(0.2)(0.2) = 0.008

20b. What is the probability that none are cherry? P(C'C'C') = 0.7(0.7)(0.7) = 0.343

20c. What is the probability that at least one is orange? 1 - P(No Orange) = 1 - 0.6(0.6)(0.6) = 1 - 0.216 = 0.784

20d. What is the probability that the last one is the first one that is lemon? P(L'L'L) = 0.9(0.9)(0.1) = 0.081

20e. What is the probability that all three are different flavors?

- P(GOC) = 0.2(0.4)(0.3) = 0.024
- P(GOL) = 0.2(0.4)(0.1) = 0.008
- P(GCL) = 0.2(0.3)(0.1) = 0.006
- P(OCL) = 0.4(0.3)(0.1) = 0.012

But there are 6 ways that each of those can occur, so add them together
and multiply by 6.

6( 0.024 + 0.008 + 0.006 + 0.012 ) = 6 ( 0.050 ) = 0.300