Question

A binomial experiment with probability of success p=0.16 and n=9 trials is conducted. What is the probability that the experiment results in fewer than 2 successes? Do not round your Intermediate computations, and round your answer to three decimal places

Answer 1

To find the probability of fewer than 2 successes in a binomial experiment with p=0.16 and n=9 trials, calculate the probabilities of 0 and 1 successes using the binomial probability formula and add them together.

Step-by-step explanation:

A binomial experiment with probability of success p=0.16 and n=9 trials is conducted. To find the probability that the experiment results in fewer than 2 successes, we need to calculate the probabilities of getting 0 successes and 1 success, and then add them together.

To calculate the probability of getting 0 successes, we use the formula: P(X=0) = (n choose 0) * (p^0) * (q^(n-0)). Here, n is the number of trials, p is the probability of success, and q is the probability of failure. Similarly, we can calculate the probability of getting 1 success using the formula: P(X=1) = (n choose 1) * (p^1) * (q^(n-1)). Finally, we add these two probabilities together to find the probability of fewer than 2 successes.

Answer 2

The probability that the experiment results in fewer than 2 successes is 0.555 to three decimal places.

Solving probability involving binomial expression.

The probability mass function for a binomial expression can be expressed as:

`P(X=k) = (^n_k) * p^k* (1-p)^(n-k)`.

Here;

• n = no. of trials = 9
• k = no. of success
• p = probability of success = 0.16
• (1 - p) = probability of failure

Now, to find the probability that the experiment results is fewer than 2 successes, we have

P(X < 2) = P(X = 0) + P(X = 1)

`P(X < 2) = (^9_0)* 0.16^0 * (1-0.16)^9 + (^9_1) * 0.16^1 * (1-0.16)^8`

Solving each term, we have:

`P(X < 2) = 1 * 0.84^9 +9* 0.16 * 0.84^8`

P(X < 2) = 0.2205 + 0.3343

P(X < 2) = 0.5548

Thus, the probability that the experiment results in fewer than 2 successes is 0.555 to three decimal places.