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

Answer:

The probability the first drawn marble will be blue is $\dfrac{1}{4}$.

The probability the second marble drawn will be yellow is $\dfrac{5}{12}$.

$P(\text{blue, then yellow}) =\dfrac{5}{48}$

Step-by-step 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:

$P_1=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}$

$P_1=\dfrac{3}{12}$

$P_1=\dfrac{1}{4}$

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:

$P_2=\dfrac{\text{Number of yellow marbles}}{\text{Total number of marbles}}$

$P_2=\dfrac{5}{12}$

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

$P(\text{blue, then yellow}) =P_1\times P_2$

$P(\text{blue, then yellow}) =\dfrac{1}{4}\times \dfrac{5}{12}$

$P(\text{blue, then yellow}) =\dfrac{5}{48}$

Therefore, the required probability is $\dfrac{5}{48}$.

Answer 2

Answer:  

Possible outcomes=12

$P(\text{Blue marble first})=\frac{1}{4}$

$P(\text{Yellow marble})=\frac{5}{12}$

$P(\text{ Blue then yellow})=\frac{5}{48}$

Step-by-step 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.

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

Now we will find probability of getting yellow marble.

$P(\text{Yellow marble})=\frac{5}{(3+4+5)} =\frac{5}{12}$

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

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

Therefore, probability of getting a blue marble and then yellow marble is $\frac{5}{48}$.