During the winter it snows 3 out of every 10 days what is the probability that it will snow, in any given week 7 days, more than 3 times?
So you want the prob that it will snow 4 times, 5 times , 6 times or 7 times
or, what you don't want is 0 days of snow, 1 day of snow, 2 days of snow or 3 days of snow
each approach requires 4 calculations, so I suggest the first method.
Add up the 4 probabilities.
let me know what you got
I got 12.6% thank you!
correct, I had the same
To find the probability that it will snow more than 3 times in a given week, we can start by finding the probability that it will snow exactly 3 times or less, and then subtracting that probability from 1.
Given that it snows 3 out of every 10 days, the probability that it will snow on any given day is 3/10. Therefore, the probability that it will not snow on any given day is 1 - 3/10 = 7/10.
To find the probability that it will snow exactly 3 times or less in a week, we can use the binomial probability formula:
P(X = k) = (n C k) * p^k * (1 - p)^(n - k)
Where:
- n is the number of trials (in this case, 7 days in a week)
- k is the number of successes (in this case, 3 or less snowy days)
- p is the probability of success on a single trial (in this case, 3/10)
- (n C k) represents the combination symbol, which calculates the number of ways to choose k successes out of n trials.
Now, let's calculate the probability that it will snow exactly 3 times or less in a week:
P(X <= 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
P(X = 0) = (7 C 0) * (3/10)^0 * (7/10)^(7 - 0) = 1 * 1 * (7/10)^7
P(X = 1) = (7 C 1) * (3/10)^1 * (7/10)^(7 - 1) = 7 * (3/10) * (7/10)^6
P(X = 2) = (7 C 2) * (3/10)^2 * (7/10)^(7 - 2) = 21 * (3/10)^2 * (7/10)^5
P(X = 3) = (7 C 3) * (3/10)^3 * (7/10)^(7 - 3) = 35 * (3/10)^3 * (7/10)^4
Summing up these probabilities gives us the probability of 3 or less snowy days:
P(X <= 3) = 1 * (7/10)^7 + 7 * (3/10) * (7/10)^6 + 21 * (3/10)^2 * (7/10)^5 + 35 * (3/10)^3 * (7/10)^4
To find the probability of more than 3 snowy days in a week, we can subtract P(X <= 3) from 1:
P(X > 3) = 1 - P(X <= 3)
Finally, you can calculate the probability using the above formula.