Compute the probability of $$ X $$ successes using the binomial formula. Round your answers to three decimal places as needed. Part: $$ 0 / 5 $$ Part 1 of 5 (a) $$ n=3, p=0.65, X=0 $$ $$ P(X)=\square $$

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To compute the probability of $$ X $$ successes using the binomial formula, we can use the formula:

$$ P(X) = \binom{n}{X} p^X (1-p)^{n-X} $$

where:
- $$ n $$ is the total number of trials,
- $$ p $$ is the probability of success in each trial,
- $$ X $$ is the number of successes.

Given:
- $$ n = 3 $$,
- $$ p = 0.65 $$,
- $$ X = 0 $$.

Substitute these values into the formula:

$$ P(X) = \binom{3}{0} (0.65)^0 (1-0.65)^{3-0} $$

$$ P(X) = 1 \times 1 \times (0.35)^3 $$

$$ P(X) = (0.35)^3 $$

Now, we can calculate the value of $$ P(X) $$ using the binomial formula.
Calculate the value by following steps:
- step0: Calculate:
  $$0.35^{3}$$
- step1: Convert the expressions:
  $$\left(\frac{7}{20}\right)^{3}$$
- step2: Use the properties of exponents:
  $$\frac{7^{3}}{20^{3}}$$
- step3: Evaluate the power:
  $$\frac{343}{20^{3}}$$
- step4: Evaluate the power:
  $$\frac{343}{8000}$$
The probability of $$ X = 0 $$ successes is $$ P(X) = 0.042875 $$ when $$ n = 3 $$, $$ p = 0.65 $$, and $$ X = 0 $$.
The probability of 0 successes is 0.043.

Compute the probability of successes using the binomial formula. Round your answers to three decimal places as needed.
Part:
Part 1 of 5
(a)

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Compute the probability of successes using the binomial formula. Round your answers to three decimal places as needed. Part: Part 1 of 5 (a)