A binomial probability experiment is conducted with the given parameters. Compute the probability of successes in the independent frials of the experiment.

(Do not round until the final answer. Then round to four decimal places as needed.)

Ask by Lane Graham. in the United States

Mar 26,2025

Question

A binomial probability experiment is conducted with the given parameters. Compute the probability of successes in the independent frials of the experiment.

(Do not round until the final answer. Then round to four decimal places as needed.)

Ask by Lane Graham. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

We start with the binomial probability formula
$$
P(x) = \binom{n}{x} p^x (1-p)^{n-x}.
$$
For this problem, $$ n = 30 $$, $$ p = 0.05 $$, and $$ x = 2 $$.

1. Calculate the binomial coefficient:
   $$
   \binom{30}{2} = \frac{30 \times 29}{2} = 435.
   $$

2. Substitute into the probability formula:
   $$
   P(2) = 435 \times (0.05)^2 \times (0.95)^{28}.
   $$

3. Compute $$ (0.05)^2 $$:
   $$
   (0.05)^2 = 0.0025.
   $$
   So, the expression becomes:
   $$
   P(2) = 435 \times 0.0025 \times (0.95)^{28}.
   $$
   
4. Multiply the constant terms:
   $$
   435 \times 0.0025 = 1.0875.
   $$
   Now we have:
   $$
   P(2) = 1.0875 \times (0.95)^{28}.
   $$

5. Compute $$ (0.95)^{28} $$ (using a calculator or appropriate software):
   $$
   (0.95)^{28} \approx 0.2388.
   $$

6. Multiply to find $$ P(2) $$:
   $$
   1.0875 \times 0.2388 \approx 0.2597.
   $$

Thus, the probability of exactly 2 successes is
$$
\boxed{0.2597}.
$$
The probability of exactly 2 successes is 0.2597.

A binomial probability experiment is conducted with the given parameters. Compute the probability of successes in the independent frials of the experiment.

(Do not round until the final answer. Then round to four decimal places as needed.)

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A binomial probability experiment is conducted with the given parameters. Compute the probability of successes in the independent frials of the experiment. (Do not round until the final answer. Then round to four decimal places as needed.)

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A binomial probability experiment is conducted with the given parameters. Compute the probability of successes in the independent frials of the experiment.

(Do not round until the final answer. Then round to four decimal places as needed.)