Determine the indicated probability for a binomial experiment with the given number of trials $n$ and the given success probability $p$.
$$n = 12 , p = 0.7 , P \text { (3 or fewer) }$$
A) 0.0002
B) 0.9983
C) 0.0017
D) 0.0095

Question

Quizplus · Accepted Answer

The probability of getting 3 or fewer successes in a binomial experiment with $n = 12$ trials and success probability $p = 0.7$ can be calculated using the binomial probability formula: $$P(X = k) = \binom{n}{k}p^k(1-p)^{n-k}$$ for $k = 0, 1, 2, 3$. Summing these probabilities gives the total probability of getting 3 or fewer successes. The correct answer is obtained through calculation or binomial distribution tables/tools, which in this case is approximately 0.0017.

Determine the Indicated Probability for a Binomial Experiment with the Given