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Anthony has two bags of marbles. the first bag contains 12 red marbles, and 8 green marbles. The second bad contains 6 red marbles, 4 blue marbles, and 8 green marbles. Anthony will randomly select 1 marble from each bag. What is the probability that he will select a red marble from each bag

Answer :

First bag:

Red = 12

Green = 8

Second bag:

Red = 6

Blue = 4

Green = 8

The probability to select a red marble from each bag can be calculated using:

[tex]P(\text{Red})=\frac{\text{ Number of reds}}{\text{ Total}}[/tex]

Now, for the first bag:

[tex]P_1(\text{Red})=\frac{12}{20}=\frac{3}{5}[/tex]

Now, for the second bag:

[tex]P_2(\text{Red})=\frac{6}{18}=\frac{1}{3}[/tex]

Both selections are independent events, so the overall probability to select a red marble from each bag is just the product of P₁ and P₂:

[tex]\begin{gathered} P(\text{Red})=P_1(\text{Red})\cdot P_2(\text{Red})=\frac{3}{5}\cdot\frac{1}{3} \\ P(\text{Red})=\frac{1}{5} \end{gathered}[/tex]

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