To find the probability, we need to consider the total number of workers and the number of workers we want to choose.
a) To find the probability of choosing all first-shift workers:
- Total number of workers = 36 + 19 = 55
- Number of ways to choose 5 workers from the first-shift workers = (36 choose 5)
So, the probability of choosing all first-shift workers is given by:
P(all first-shift workers) = (number of ways to choose 5 workers from the first-shift workers) / (total number of workers choose 5)
b) To find the probability of choosing all second-shift workers:
- Total number of workers = 55
- Number of ways to choose 5 workers from the second-shift workers = (19 choose 5)
So, the probability of choosing all second-shift workers is given by:
P(all second-shift workers) = (number of ways to choose 5 workers from the second-shift workers) / (total number of workers choose 5)
c) To find the probability of choosing six first-shift workers:
- Total number of workers = 55
- Number of ways to choose 6 workers from the first-shift workers = (36 choose 6)
So, the probability of choosing six first-shift workers is given by:
P(six first-shift workers) = (number of ways to choose 6 workers from the first-shift workers) / (total number of workers choose 5)
d) To find the probability of choosing four second-shift workers:
- Total number of workers = 55
- Number of ways to choose 4 workers from the second-shift workers = (19 choose 4)
So, the probability of choosing four second-shift workers is given by:
P(four second-shift workers) = (number of ways to choose 4 workers from the second-shift workers) / (total number of workers choose 5)
To calculate these probabilities, we need to use combinations (n choose r) which can be calculated using the formula:
n! / (r! * (n - r)!)
Now, you can substitute the appropriate values into the formulas to find the probabilities for each case.