Quote (TDW13 @ Apr 10 2023 12:57am)
The total number of days in which the events can occur is 30 days. Out of these 30 days, there are 8 days you do not want the events to occur. Therefore, the number of favorable outcomes (the events occurring on one of those 8 days) is 22.
The probability of the event occurring on one of those 8 days can be calculated as:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 22/30
Probability = 11/15
Therefore, the probability of the event occurring on one of those 8 days is 11/15 or approximately 0.73.
As a ratio, the probability can be expressed as 11:15.
As a percentage, the probability can be expressed as 73.33%.
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To find the probability of an event occurring on one of the 8 specified days, we can use the concept of combinations.
First, we have 30 days and want to choose 2 days for the events to occur. The number of ways to do this is represented by the combination formula:
C(n, k) = n! / (k!(n-k)!)
where n = total number of days (30), k = number of days to choose (2), and ! denotes the factorial.
C(30, 2) = 30! / (2!(30-2)!)
C(30, 2) = 30! / (2! * 28!)
C(30, 2) = (30 * 29) / (2 * 1)
C(30, 2) = 870
So, there are 870 possible combinations for the events to occur in the 30-day period.
Now, we need to find the number of combinations where at least one event occurs on one of the 8 specified days. We can break this down into two scenarios:
One event occurs on one of the 8 days, and the other event occurs on one of the remaining 22 days.
C(8, 1) * C(22, 1) = 8! / (1!(8-1)!) * 22! / (1!(22-1)!)
C(8, 1) * C(22, 1) = (8 * 22) = 176
Both events occur on the 8 specified days.
C(8, 2) = 8! / (2!(8-2)!)
C(8, 2) = (8 * 7) / (2 * 1)
C(8, 2) = 28
Now, we add the results from both scenarios:
Total favorable combinations = 176 (one event on 8 days) + 28 (both events on 8 days) = 204
Now, we find the probability by dividing the favorable combinations by the total possible combinations:
Probability = Favorable combinations / Total possible combinations
Probability = 204 / 870
As a decimal, this is approximately:
Probability ≈ 0.23448275862068965
As a percentage:
Probability ≈ 23.45%
As a ratio:
Probability ≈ 204:870
You can further simplify this ratio by dividing both numbers by their greatest common divisor (GCD), which is 6 in this case:
Probability ≈ 34:145
So, the probability of at least one event occurring on one of the 8 specified days is approximately 23.45% or 34:145 as a ratio.