Answer:
P (g1, g2) = P(g1) * P(g2) = 1/2 * 1/2 = 1/4
P (r1, r2) = P(r1) * P(r2) = 1/5 * 1/5 = 1/25
P ( b1, g1 or g1 b2) = 3/20 + 3/20 = 6/20 = 3/10
P ( b1, g1 or g1 b2) = 1/10 + 1/10 = 2/10 = 1/5
Step-by-step explanation:
How many marbles are there?
5 green, 3 black, and 2 red marbles = 10 marbles
P ( green marbles) = green/ total = 5/10 = 1/2
Then she puts it back, so there are still 10 marbles
P (2nd marble is green) = green/ total = 5/10 = 1/2
These are independent events ( since the marble is replaced)
P (g1, g2) = P(g1) * P(g2) = 1/2 * 1/2 = 1/4
P ( red marble) = red/ total = 2/10 = 1/5
Then she puts it back, so there are still 10 marbles
P (2nd marble is red) = red/ total = 2/10 = 1/5
These are independent events ( since the marble is replaced)
P (r1, r2) = P(r1) * P(r2) = 1/5 * 1/5 = 1/25
P ( black marble) = black/ total = 3/10
Then she puts it back, so there are still 10 marbles
P (2nd marble is green) = green/ total = 5/10 = 1/2
These are independent events ( since the marble is replaced)
P (b1, g2) = P(b1) * P(g2) = 3/10 * 1/2 = 3/20
This is if order matters, but I will assume order does not matter since the key word then is not there it just says and
If order doesn't matter, just that she has a black and green marble
The we multiply it by 2 because
P (b2, g1) = P(b2) * P(g1) = 1/2 * 3/10 = 3/20
We add the probabilities when it is or
P ( b1, g1 or g1 b2) = 3/20 + 3/20 = 6/20 = 3/10
P ( green marble) = green/ total = 5/10=1/2
Then she puts it back, so there are still 10 marbles
P (2nd marble is red) = red/ total = 2/10 = 1/5
These are independent events ( since the marble is replaced)
P (g1, r2) = P(g1) * P(r2) = 1/2 * 1/5 = 1/10
This is if order matters but I will assume order does not matter since the key word then is not there it just says and
If order doesn't matter, just that she has a green and red marble
The we multiply it by 2 because
P (r1, g2) = P(r1) * P(g2) = 1/5 * 1/2 = 1/10
We add the probabilities when it is or
P ( b1, g1 or g1 b2) = 1/10 + 1/10 = 2/10 = 1/5
