Question

A dog completes a trick 8 out of 20 times. What is the probability the dog completes a trick 12 out of 20 times

Answer 1

To find the probability that the dog completes a trick 12 out of 20 times, we need to use the binomial probability formula.

The formula for the probability of getting exactly k successes out of n trials, with a probability p of success on each trial, is given by:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Here, n = 20 (total number of trials), k = 12 (desired number of successes), and p = 8/20 = 0.4 (probability of success on each trial).

Using the formula, we can calculate:

P(X = 12) = (20 choose 12) * (0.4)^12 * (1 - 0.4)^(20-12)

Using a combination (n choose k) calculator, we find that (20 choose 12) = 125,970.

P(X = 12) = 125,970 * (0.4)^12 * (0.6)^8

Calculating this expression, we find:

P(X = 12) ≈ 0.2337

So, the probability that the dog completes a trick 12 out of 20 times is approximately 0.2337, or 23.37%.