Final answer:
The binomial probability of getting exactly one success in two trials when the success probability is 0.70 is calculated using the binomial formula and is 0.42.
Step-by-step explanation:
The question given is a binomial probability problem where we are asked to find the probability of exactly 1 success in 2 trials, with the probability of success in each trial being 0.7. The binomial formula for calculating this probability is P(X = x) = nCx * p^x * q^(n-x), where P(X = x) denotes the probability of getting exactly x successes in n trials, nCx represents the binomial coefficient, p is the probability of success on any given trial, and q is the probability of failure (q = 1-p).
Given n = 2, x = 1, and p = 0.70, we find:
nCx = 2C1 = 2 (There are 2 ways of picking 1 success from 2 trials)
p^x = 0.70^1 = 0.70
q^(n-x) = (1 - 0.70)^(2-1) = 0.30^1 = 0.30
So the binomial probability P(X = 1) = 2 * 0.70 * 0.30 = 0.42.
Therefore, the binomial probability of getting exactly one success in two trials when the success probability is 0.70 is 0.42.