Question

A bag contains 7 orange marbles, 20 green marbles, and 11 blue marbles.

If two marbles are chosen randomly from the bag one at a time and put back, what is the probability that the first marble is green and the second marble is blue?

Answer 1

There are 38 total marbles and each marble is put back after being chosen randomly, therefore, the probability the first marble is green is\[\frac{20}{38}\]The probability the second marble is blue is:
\[\frac{11}{38}\]

Each event is independent. What do we do with independent probabilities to find the total probability of both events?

Answer 2

add them?

Answer 3

Not add.

Answer 4

multiply?

Answer 5

Yes

Answer 6

does the denominator stay the same?

Answer 7

Simplify before multiplying

Answer 8

When you multiply fractions you multiply the numerators, then you multiply the denominators.

Answer 9

Only when adding do they stay the same. Reduce the fractions before multiplying

Answer 10

10/19 x 11/38 ?

Answer 11

You can reduce the fraction even more than that

Answer 12

\[\frac{10}{19} \times \frac{19}{38} = \frac{10}{38} \times \frac{11}{19}\]

Answer 13

55/361 ?