Final answer:
To find the probability that 2 or 3 tickets are completed in one hour, we use the concept of binomial distribution. By calculating P(X = 2) and P(X = 3) using the binomial probability formula, we can add these probabilities together to get the final result.
Step-by-step explanation:
To find the probability that 2 or 3 tickets are completed in one hour, we can use the concept of binomial distribution. Let's define success as closing a ticket and failure as not closing a ticket. The probability of success, p, is 3 tickets closed per hour divided by the total number of possible outcomes, which is 3 tickets closed plus 0 tickets closed. Therefore, p = 3 / (3 + 0) = 1.
Now, we can use the binomial probability formula to calculate the probability of getting exactly 2 or 3 successes in one hour. The formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of getting k successes
- n is the total number of trials
- k is the number of successes
- C(n, k) is the number of combinations of n things taken k at a time
- p is the probability of success
In this case, n = 3 (as we are considering 2 or 3 successes), k = 2 and k = 3, and p = 1.
P(X = 2) = C(3, 2) * 1^2 * (1 - 1)^(3 - 2) = 3
P(X = 3) = C(3, 3) * 1^3 * (1 - 1)^(3 - 3) = 1
Now, to find the probability that 2 or 3 tickets are completed in one hour, we need to add these two probabilities together: P(X = 2 or 3) = P(X = 2) + P(X = 3) = 3 + 1 = 4.
Therefore, the probability that 2 or 3 tickets are completed in one hour is 4.