Question

An office in Albuquerque has 24 workers including management. Eight of the workers commute to work from the west side of the Rio Grande River. Suppose six of the office workers are randomly selected. (Round your answers to 4 decimal places, e.g. 0.2153.) a. What is the probability that all six workers commute from the west side of the Rio Grande? P(x = 6) = b. What is the probability that none of the workers commute from the west side of the Rio Grande? P(x = 0) = c. Which probability from parts (a) and (b) was greatest? d. What is the probability that half of the workers do not commute from the west side of the Rio Grande? P(x = 3) =

Answer 1

To calculate the probability of all 6 workers commuting from the west side, multiply the probabilities together. The probability of none of the workers commuting is found by subtracting the probability of all 6 workers commuting from 1. Compare the probabilities to determine which one is greater. To find the probability of half of the workers not commuting, multiply the probabilities together.

Step-by-step explanation:

To answer part a, we can use the concept of probability. There are 8 workers who commute from the west side of the Rio Grande River out of a total of 24 workers. So the probability of selecting a worker who commutes from the west side is 8/24. Since we are selecting 6 workers, we need to multiply the probabilities together: (8/24) * (8/24) * (8/24) * (8/24) * (8/24) * (8/24). This gives us the probability of all 6 workers commuting from the west side of the river.

For part b, we want to find the probability of none of the workers commuting from the west side. This can be calculated by subtracting the probability of all 6 workers commuting from 1. So the probability of none of the workers commuting is 1 - (8/24) * (8/24) * (8/24) * (8/24) * (8/24) * (8/24).

For part c, compare the probabilities from parts a and b to determine which one is greater.

To calculate the probability of half of the workers not commuting, we need to select 3 workers out of the 16 who do not commute and 3 workers out of the total 24 workers. The probability can be calculated by multiplying the probabilities together: (16/24) * (15/23) * (14/22) * (8/24) * (8/24) * (8/24).