When n = 5 and p = 0.8, we have P(5) = . Therefore, P(r = 5) =

The question seems to be referring to a binomial distribution problem. However, it's incomplete. The binomial distribution formula is P(r) = C(n, r) * (p^r) * ((1-p)^(n-r)), where:

• P(r) is the probability of r successes,
• C(n, r) is the combination of n items taken r at a time,
• p is the probability of success,
• n is the number of trials, and
• r is the number of successes.

Given n = 5 (number of trials) and p = 0.8 (probability of success), and we want to find P(r = 5), or the probability of 5 successes.

Let's plug these values into the formula:

P(5) = C(5, 5) * (0.8^5) * ((1-0.8)^(5-5))

Step 1: Calculate C(5, 5), which is the number of ways to choose 5 successes from 5 trials. This is simply 1.

Step 2: Calculate 0.8^5, which is the probability of getting 5 successes. This equals 0.32768.

Step 3: Calculate (1-0.8)^(5-5), which is the probability of getting 0 failures. This equals 1.

Step 4: Multiply the results from steps 1, 2, and 3 together:

P(5) = 1 * 0.32768 * 1 = 0.32768

Therefore, P(r = 5) = 0.32768, or approximately 32.77% when expressed as a percentage.