Final answer:
A binomial experiment is one that satisfies the conditions of having a fixed number of trials, two possible outcomes (success and failure), and independent and identical conditions for each trial. In this case, we have two trials with a success probability of 0.4. The answer provides step-by-step explanations for each part of the question, including drawing a tree diagram, calculating probabilities, and computing the expected value, variance, and standard deviation.
Step-by-step explanation:
A binomial experiment is one that satisfies the conditions of having a fixed number of trials, two possible outcomes (success and failure), and independent and identical conditions for each trial. In this case, we have two trials with a success probability of 0.4. To answer the questions:
a. You can draw a tree diagram to represent this experiment. Each branch represents a trial, and the probabilities of success and failure are labeled on the branches.
b. To compute the probability of one success (f(1)), you can use the binomial probability formula: P(X = 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 you want to find the probability for. In this case, n = 2, p = 0.4, q = 0.6, and k = 1. Plug in these values and calculate.
c. To compute f(0), you can use the same formula with k = 0.
d. To compute f(2), you can use the same formula with k = 2.
e. To compute the probability of at least one success, you can find the probability of getting 1 success or 2 successes, and add them together.
f. To compute the expected value (E(X)), you can use the formula E(X) = n * p.
g. To compute the variance (Var(X)), you can use the formula Var(X) = n * p * q.
h. To compute the standard deviation (σ), you can take the square root of the variance.