Question

Regina has a bag of marbles that contains 3 blue marbles, 4 red marbles, and 5 yellow marbles. She draws one marble, then replaces it, and draws one more.

There are possible outcomes.

The probability the first drawn marble will be blue is .

The probability the second marble drawn will be yellow is .

So, P(blue, then yellow) =

Answer 1

The probability the first drawn marble will be blue is
`(1)/(4)`.

The probability the second marble drawn will be yellow is
`(5)/(12)`.

`P(\text{blue, then yellow}) =(5)/(48)`

Explanation:

From the given information, it is clear that

Number of blue marbles = 3

Number of red marbles = 4

Number of yellow marbles = 5

Total number of marbles = 3+4+5 = 12

The probability the first drawn marble will be blue is:

`P_1=\frac{\text{Number of blue marbles}}{\text{Total number of marbles}}`

`P_1=(3)/(12)`

`P_1=(1)/(4)`

She draws one marble, then replaces it, and draws one more. It means total number of marbles remains same.

The probability the second marble drawn will be yellow is:

`P_2=\frac{\text{Number of yellow marbles}}{\text{Total number of marbles}}`

`P_2=(5)/(12)`

We need to find the value of P(blue, then yellow).

`P(\text{blue, then yellow}) =P_1* P_2`

`P(\text{blue, then yellow}) =(1)/(4)* (5)/(12)`

`P(\text{blue, then yellow}) =(5)/(48)`

Therefore, the required probability is
`(5)/(48)`.

Answer 2

Possible outcomes=12

`P(\text{Blue marble first})=(1)/(4)`

`P(\text{Yellow marble})=(5)/(12)`

`P(\text{ Blue then yellow})=(5)/(48)`

Explanation:

We can see these two events are independent as Regina replaced marble after drawing one marble.

We can find possible outcomes by adding number of blue, red and yellow marbles.

`\text{Possible outcomes}=3+4+5=12`

Let us find probability of getting a blue marble on first draw.

`P(\text{Blue marble})=(3)/((3+4+5)) =(3)/(12) =(1)/(4)`

Now we will find probability of getting yellow marble.

`P(\text{Yellow marble})=(5)/((3+4+5)) =(5)/(12)`

We can find probability of getting a blue marble and then yellow marble by multiplying both probabilities.

`P(\text{ Blue then yellow})=(1)/(4)* (5)/(12) =(5)/(48)`

Therefore, probability of getting a blue marble and then yellow marble is
`(5)/(48)`.