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In an experiment with probability function f(x) is binomially distributed with probability p that an attribute occurs at a single trial. If in four trials of the experiment, the attribute occurs four times with probability 16/81, find the value of p

User Abdulqadir
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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

User Real Quick
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