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.
\[
P(X \leq 2), n=6, p=0.6
\]

Step 1 ：We are given a binomial random variable $X$ with parameters $n=6$ and $p=0.6$. We are asked to find the probability that $X$ takes on a value less than or equal to 2, i.e., $P(X \leq 2)$.

Step 2 ：This is equivalent to finding the cumulative distribution function (CDF) of $X$ at 2. The CDF of a binomial random variable at a point $k$ is given by the sum of the probabilities of $X$ taking on all values from 0 to $k$. In other words, we need to calculate $P(X=0) + P(X=1) + P(X=2)$.

Step 3 ：The probability mass function (PMF) of a binomial random variable is given by: $P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$, where $\binom{n}{k}$ is the binomial coefficient, which can be calculated as $\frac{n!}{k!(n-k)!}$, and $p$ is the probability of success on a single trial.

Step 4 ：So, we need to calculate and sum up $P(X=0)$, $P(X=1)$, and $P(X=2)$ using the above formula.

Step 5 ：By substituting the given values into the formula, we get $P(X \leq 2) = 0.1792$.

Step 6 ：Final Answer: The probability that a binomial random variable $X$ with parameters $n=6$ and $p=0.6$ takes on a value less than or equal to 2 is approximately \(\boxed{0.1792}\).