Using the Binomial distribution,
If $n=5$ and $p=0.8$, find $P(x=5)$

Step 1 ：We are given a problem involving the Binomial distribution, where the number of trials (n) is 5, the probability of success on a single trial (p) is 0.8, and we are asked to find the probability of getting 5 successes (x=5).

Step 2 ：The formula for the binomial distribution is: \(P(x) = C(n, x) * p^x * (1-p)^(n-x)\), where \(C(n, x)\) is the number of combinations of n items taken x at a time, \(p^x\) is the probability of success raised to the power of the number of successes, and \((1-p)^(n-x)\) is the probability of failure raised to the power of the number of failures.

Step 3 ：Plugging in the given values into this formula, we get \(P(5) = C(5, 5) * 0.8^5 * (1-0.8)^(5-5)\).

Step 4 ：Calculating the combinations, \(C(5, 5)\), we get 1.

Step 5 ：Calculating the probability of success, \(0.8^5\), we get 0.32768.

Step 6 ：Calculating the probability of failure, \((1-0.8)^(5-5)\), we get 1.

Step 7 ：Multiplying these values together, we get \(P(5) = 1 * 0.32768 * 1 = 0.32768\).

Step 8 ：Final Answer: The probability of getting 5 successes in 5 trials when the probability of success on a single trial is 0.8 is \(\boxed{0.32768}\).