Answer:
Explanation:
A binomial probability function has two parameters: n, the number of trials and p, the probability of success (or occurrence of the attribute) in a single trial.
In this case, we are given that the attribute occurs four times in four trials, with probability 16/81. Using this information, we can use the binomial probability formula to find the value of p:
P(k) = (n choose k) * p^k * (1-p)^(n-k)
Where k is the number of successes in n trials, and (n choose k) is the binomial coefficient, which is the number of ways to choose k items from n items without replacement.
In this case,
k = 4 (the attribute occurs four times)
n = 4 (there are four trials)
P(k) = 16/81
We can use this equation to find the value of p:
(4 choose 4) * p^4 * (1-p)^(4-4) = 16/81
1 * p^4 * (1-p)^0 = 16/81
p^4 = 16/81
p = √(16/81)
p = √(4/81)
p = √(1/81)
p = 1/9
The value of p is 1/9
This means that in a single trial of the experiment, the probability of the attribute occurring is 1/9 or about 0.111