Answer:
Possible outcomes=12
[tex]P(\text{Blue marble first})=\frac{1}{4}[/tex]
[tex]P(\text{Yellow marble})=\frac{5}{12}[/tex]
[tex]P(\text{ Blue then yellow})=\frac{5}{48}[/tex]
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.
[tex]\text{Possible outcomes}=3+4+5=12[/tex]
Let us find probability of getting a blue marble on first draw.
[tex]P(\text{Blue marble})=\frac{3}{(3+4+5)} =\frac{3}{12} =\frac{1}{4}[/tex]
Now we will find probability of getting yellow marble.
[tex]P(\text{Yellow marble})=\frac{5}{(3+4+5)} =\frac{5}{12}[/tex]
We can find probability of getting a blue marble and then yellow marble by multiplying both probabilities.
[tex]P(\text{ Blue then yellow})=\frac{1}{4}* \frac{5}{12} =\frac{5}{48}[/tex]
Therefore, probability of getting a blue marble and then yellow marble is [tex]\frac{5}{48}[/tex].
Answer:
The probability the first drawn marble will be blue is [tex]\dfrac{1}{4}[/tex].
The probability the second marble drawn will be yellow is [tex]\dfrac{5}{12}[/tex].
[tex]P(\text{blue, then yellow}) =\dfrac{5}{48}[/tex]
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:
[tex]P_1=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}[/tex]
[tex]P_1=\dfrac{3}{12}[/tex]
[tex]P_1=\dfrac{1}{4}[/tex]
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:
[tex]P_2=\dfrac{\text{Number of yellow marbles}}{\text{Total number of marbles}}[/tex]
[tex]P_2=\dfrac{5}{12}[/tex]
We need to find the value of P(blue, then yellow).
[tex]P(\text{blue, then yellow}) =P_1\times P_2[/tex]
[tex]P(\text{blue, then yellow}) =\dfrac{1}{4}\times \dfrac{5}{12}[/tex]
[tex]P(\text{blue, then yellow}) =\dfrac{5}{48}[/tex]
Therefore, the required probability is [tex]\dfrac{5}{48}[/tex].
