Final answer:
- a. The probability of no one being involuntarily denied boarding is 26%.
- b. The probability of at least one person being involuntarily denied boarding is 74%.
- c. The probability of at least two persons being involuntarily denied boarding is 0%.
Step-by-step explanation:
To calculate the probabilities in the given scenario, we need to use the rate of involuntarily denying boarding provided. Let's break down each part:
**a. To find the probability that no one is involuntarily denied boarding in the next 10,000 passengers, we can use the rate given. The rate is 0.74 per 10,000 passengers. This means that out of 10,000 passengers, 0.74 will be involuntarily denied boarding.
Therefore, the probability of no one being involuntarily denied boarding is 1 minus the rate: 1 - 0.74 = 0.26 or 26%.
**b. To find the probability of at least one person being involuntarily denied boarding, we need to consider the complement of the probability of no one being denied. We found in part a that the probability of no one being denied is 0.26 or 26%. Therefore, the probability of at least one person being involuntarily denied boarding is 1 minus the probability of no one being denied:
1 - 0.26 = 0.74 or 74%.
**c. To find the probability of at least two persons being involuntarily denied boarding, we need to consider the complement of the probability of no one being denied and the probability of only one person being denied.
We found in part a that the probability of no one being denied is 0.26 or 26%. We can use the same rate to find the probability of only one person being denied, which is 0.74%.
Therefore, the probability of at least two persons being involuntarily denied boarding is 1 minus the probability of no one being denied and the probability of only one person being denied:
1 - 0.26 - 0.74 = 0 or 0%.