Question

One bag of marbles contains 2 black , 3 red , and 5 white marbles . A second bag contains 3 white and 2 black marbles . What is the probability of selecting one marble from each bag and that they are not both black.

Please help!!

Answer 1

NOT BOTH BLACK = 1-2/25 = 23/25

Explanation:

Bag 1 : 8 non-black out of 10

P(1) = 8/10

Bag 2: 3 non-black out of 10

P(2)=3/5

Probability of both independent events happening can be calculated using the multiplication rule

P(1) and P(2) = P(1)*P(2) = 8/10 * 3/5 = 24/50 = 12/25 (both are not black, or none is black)

Interpretating not both black meaning at most one black, then

we calculate the probability of both are black,

P(1) = 2/10

P(2) = 2/5

Probability that both balls are black can be calculated using the multiplication rule

P(1) and P(2) = 2/10 * 2/5 = 2/25

Probability that NOT BOTH BLACK = 1-2/25 = 23/25, i.e. at most one black