Question

Consider a binomial experiment with n = 5 trials and the probability of success on a single trial is p = 0.30. If R denotes the number of successes in n trials, calculate P(R is greater than or equal to 1).

a) P(R = 0)
b) P(R ≥ 1)
c) P(R < 1)
d) P(R = 5)

Answer 1

The probability of getting no successes in 5 trials is 0.16807. The probability of getting at least one success is 0.83193. The probability of getting exactly 5 successes is 0.

Step-by-step explanation:

First, let's calculate the probability of getting no successes in 5 trials (P(R = 0)). To do this, we use the binomial probability formula:

P(R=k) = (nCk)(p^k)(q^(n-k)), where n is the number of trials, p is the probability of success, q is the probability of failure (1-p), and k is the number of successes.

In this case, n = 5, p = 0.30, and q = 0.70. So, P(R = 0) = (5C0)(0.30^0)(0.70^(5-0)) = 0.16807.

Next, let's calculate the probability of getting at least one success (P(R ≥ 1)). We can use the complement rule to find this probability: P(R ≥ 1) = 1 - P(R = 0) = 1 - 0.16807 = 0.83193.

Therefore, the answers to the given questions are:

a) P(R = 0) = 0.16807

b) P(R ≥ 1) = 0.83193

c) P(R < 1) = P(R = 0) = 0.16807

d) P(R = 5) = 0 (since the probability of getting 5 successes is 0 in this case).