Question

If n=5 and p=0.2, find P(x=3) Give at least 4 decimal
places.

Answer 1

Using the binomial probability formula with n=5 and p=0.2, the probability P(x=3) is calculated as 0.0512, correct to four decimal places.

Step-by-step explanation:

If n=5 and p=0.2, to find P(x=3), we can use the binomial probability formula:

P(x = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

• C(n, k) is the number of combinations of n things taken k at a time.
• p is the probability of success on a single trial.
• k is the number of successes for which we are finding the probability.
• n is the number of trials.

Let's calculate it:

C(5, 3) = 5! / (3!*(5-3)!) = 10

P(x = 3) = 10 * (0.2)^3 * (0.8)^(5-3) = 10 * 0.008 * 0.64 = 0.0512

Therefore, P(x=3) when n=5 and p=0.2 is 0.0512, accurate to four decimal places.