Eastern Airlines knows that 20% of its customer fly first class,20% fly business class, and the rest fly coach. Of those customers who fly first class,70% are from the East Coast while 30% are from elsewhere. In addition, of those customers who fly business class, 50% are from the East Coast and 50% are from elsewhere, Finally, of those customers that fly coast class,75% are from elsewhere and 25% are from the East Coast.
1- Construct a probability tree for this problem.
2- Construct a probability table for this problem.
3- Determine the probability that a customer from the East Coast will fly first class.
4- What is the probability that a customer will be from the East Coast?
1- To construct a probability tree for this problem, we can start from the top with the three categories: First Class, Business Class, and Coach. Then, we can split each category into two branches: East Coast and Elsewhere. The branches will represent the probabilities associated with each category and location.
Here is the probability tree:
```
First Class
/ \
East Coast Elsewhere
| |
70% 30%
| |
Business Class Business Class
/ \
East Coast Elsewhere
| |
50% 50%
| |
Coach Coach
East Coast Elsewhere
| |
25% 75%
| |
```
2- To construct a probability table, we can list the categories and locations as rows and columns, respectively. Then, we can fill in the corresponding probabilities based on the information given.
```
| First Class | Business Class | Coach |
---------------------------------------------------------
East Coast | 0.14 | 0.10 | 0.0375|
---------------------------------------------------------
Elsewhere | 0.06 | 0.10 | 0.1125|
---------------------------------------------------------
```
3- To determine the probability that a customer from the East Coast will fly first class, we can look at the probability table. We find that the probability of a customer from the East Coast flying first class is 0.14 or 14%.
4- To find the probability that a customer will be from the East Coast, we can add up the probabilities from the probability table for each category.
```
Probability = 0.14 (First Class) + 0.10 (Business Class) + 0.0375 (Coach) = 0.2775 or 27.75%
```
Therefore, the probability that a customer will be from the East Coast is 27.75%.