Question

A bag contains 2 red marbles and 3 black marbles. If Abby picks a marble without looking, returns it to the bag, and

then draws a second marble, what is the probability that both marbles are red? Give the answer as a fraction in
simplest form.

Answer 1

4/25

Explanation:

i got it right

Answer 2

We have been given that a bag contains 2 red marbles and 3 black marbles. Abby picks a marble without looking, returns it to the bag, and then draws a second marble. We are asked to find the probability that both marbles are red.

Let
`P(A)` be probability of getting a red marble on 1st draw and
`P(B)` be probability of getting a red marble on 2nd draw.

Number of red marbles = 2

Total number of marbles =
`2+3=5`.

`P(A)=\frac{\text{Number of red marbles}}{\text{total marbles}}`

`P(A)=(2)/(5)`

Since Abby returns the marble into the bag, so number of marbles will not change. This means that probability of both events is independent.

`P(B)=\frac{\text{Number of red marbles}}{\text{total marbles}}`

`P(B)=(2)/(5)`

When two events are independent, then their probability is
`P(\text{A and B})=P(A)* P(B)`

`P(\text{A and B})=(2)/(5)* (2)/(5)`

`P(\text{A and B})=(4)/(25)`

Therefore, the probability that both marbles are red would be
`(4)/(25)`.