posted by katie .
A box contains three black balls and two gold balls. A ball is selected at random, its color is recorded, and it is then replaced. A second ball is then selected at random and its color recorded. The outcome associated with this type of selection is an ordered pair (first draw, second draw).
a. List a sample space for this experiment.
b. What is the probability that both balls are black?
c. What is the probability that both balls are gold?
d. Why doesn’t the sum of the probabilities in parts (b) and (c) total 1?
I'm not sure what you mean by sample space.
However, the probability of a gold ball is 2/5 and the probability of a black ball is 3/5.
The probability of two or more events both occurring is found by multiplying the individual probabilities.
They don't total 1, because they don't include the probability of drawing black-gold or gold-black combinations.
I hope this helps.