# Assume that a procedure yields a binomial distribution with n=3 trials and a probability of success of p= 0.90. Use a binomial probability table to find the probability that the number of successes x is exactly 1.

## Assume the random variable

X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X = 2), n = 8, p = 0.2

## To find the probability that the number of successes (x) is exactly 1, we can use the binomial probability formula:

P(x) = nCx * p^x * q^(n-x)

Where:
- n is the total number of trials
- p is the probability of success in each trial
- q is the probability of failure in each trial (q = 1 - p)
- nCx is the number of combinations of n items taken x at a time

In this case, n = 3 and p = 0.90. Therefore, q = 1 - p = 1 - 0.90 = 0.10.

Using the binomial probability table, we can find the probability:
P(x = 1) = 3C1 * 0.90^1 * 0.10^(3-1)

From the binomial probability table (or by calculations):
3C1 = 3
0.90^1 = 0.90
0.10^2 = 0.01

P(x=1) = 3 * 0.90 * 0.01
= 0.027

So, the probability that the number of successes x is exactly 1 is 0.027 or 2.7%.

## To find the probability that the number of successes x is exactly 1, we can use a binomial probability table. Here are the steps to calculate it:

1. Look for a binomial probability table online or in a statistics textbook. These tables provide the probabilities for different values of n, p, and x.

2. In the table, locate the row that corresponds to the given number of trials, n = 3.

3. Find the column for the probability of success, p = 0.90.

4. Look under the column for x = 1 (number of successes).

5. The value in the cell where the row and column intersect represents the probability of exactly one success.

Note that the binomial probability tables usually provide cumulative probabilities, meaning they show the probabilities for a range of values from 0 up to the given value. However, since we are interested in the probability of exactly one success, you just need to find the value for x = 1.

Using the binomial probability table, you should find the probability of exactly one success for n = 3 trials and a probability of success p = 0.90.