Answer:
P(red and blue) = 0.1667
Step-by-step explanation:
Let A represent choosing a red marble, there are 3 red marbles
Let B represent choosing a blue marble, there are 4 blue marbles
There are 12 total marbles
Then...
P(A) = 3/12
P(B) = 4/12
choosing the first one, then replacing means the first choice has no effect on the probabilities of the second choice, so the situation is independent.
When calculating the probability of independent events, you multiply the probabilities together. There are 2 scenarios where we can get a red and blue marble..
Choosing a red, then a blue marble, the probability is
(3/12)( 4/12) = 12/144 = 1/12
Choosing a blue, then a red marble, the probability is
(4/12)(3/12) = 12/144 = 1/12
So we have a
(1/12) + (1/12) = 2/12 = 1/6 chance for that to happen, to
P(A and B) = 1/6 = 0.1667
