10% of a group is left handed. If a random sample of 12 switches is selected, what is the probability of exactly two of the switches being defective? (Use Binomial Distribution Formula)

Assuming that 10% is the probability of a switch being defective (since left-handedness has nothing to do with the problem):

For a binomial distribution, probability (r out of n) = (nCr) (p) ^r (q) ^ (1-r)

p = 10% = 0.1, q = 1 - p = 0.9

r = 2 switches, n = total of 12 switches

probability = (12C2) (0.1) ^2 (0.9) ^ (12-2)

probability = 66 (0.1) ^2 (0.9) ^10

probability = 0.23