To solve this problem, we can use the binomial probability distribution, which calculates the probability of a certain number of successes (in this case, black guinea pigs) in a given number of trials (in this case, the number of offspring).
The probability of producing a black offspring from two heterozygous black guinea pigs is 3/4, since there are three possible genotypes that result in black fur (BB, Bb, and bB), and only one possible genotype that results in white fur (bb).
Using the binomial probability formula, the probability of getting two black offspring out of three is:
P = (3 choose 2) * (3/4)^2 * (1/4)^1
P = 3 * 9/16 * 1/4
P = 27/64
Therefore, the probability of producing two black and one white offspring among three is 27/64, or approximately 0.42.