if the probability of a swan drowning is .27, find the probability of exactly 4 out of the 7 swans drowning.
To find the probability of exactly 4 out of the 7 swans drowning, we can use the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes
- n is the total number of trials or observations
- k is the number of desired successes
- p is the probability of success on a single trial
- (1-p) is the probability of failure on a single trial
- C(n, k) is the binomial coefficient, also known as "n choose k"
In this case:
- n = 7 (total number of swans)
- k = 4 (desired number of swans drowning)
- p = 0.27 (probability of a swan drowning)
Now we can calculate the probability:
P(X = 4) = C(7, 4) * 0.27^4 * (1-0.27)^(7-4)
To calculate the binomial coefficient C(7, 4):
C(7, 4) = 7! / (4! * (7-4)!)
After substituting the values into the equation, you can simplify and calculate the final probability.