Question

Airlines are considering 14 new routes, with 3 in FL, 7 in California, and 4 in Texas. If the airline selects 4 new routes, what is the probability that 2 are in FL and 2 in Texas?

a) 3/7

b) 3/14

c) 1/7

d) 1/14

Answer 1

To find the probability that 2 new routes are in FL and 2 are in TX out of the total 4 new routes selected from 14 options, you can use the combination formula to calculate the probability. The probability is 18/1001, which is approximately 0.018.

Step-by-step explanation:

To find the probability that 2 new routes are in Florida and 2 are in Texas, we need to calculate the number of ways we can select 2 routes from Florida and 2 routes from Texas out of the total 4 routes selected.

We can use the combination formula to calculate this.

1. Calculate the number of ways to select 2 routes from Florida: C(3, 2) = 3
2. Calculate the number of ways to select 2 routes from Texas: C(4, 2) = 6
3. Calculate the total number of ways to select 4 routes: C(14, 4) = 1001
4. Calculate the probability: (number of favorable outcomes) / (total number of outcomes) = (3 * 6) / 1001 = 18 / 1001

Therefore, the probability that 2 new routes are in Florida and 2 are in Texas is 18/1001 which is approximately 0.018.