Answer:
[tex]\dfrac{11}{30}[/tex]
Step-by-step explanation:
Urn U1: 3 red and 2 yellow marbles, in total 5 marbles.
The probability to select red marble is [tex]\dfrac{3}{5}=0.6.[/tex]
Urn U2: 3 red and 7 yellow marbles, in total 10 marbles.
The probability to select red marble is [tex]\dfrac{3}{10}=0.3.[/tex]
Urn U1: 1 red and 4 yellow marbles, in total 5 marbles.
The probability to select red marble is [tex]\dfrac{1}{5}=0.2.[/tex]
The probability to choose each urn is the same and is equal to [tex]\frac{1}{3}.[/tex]
Thus, the probability that the marble is red is
[tex]\dfrac{1}{3}\cdot 0.6+\dfrac{1}{3}\cdot 0.3+\dfrac{1}{3}\cdot 0.2=\dfrac{1.1}{3}=\dfrac{11}{30}.[/tex]
