Question

A room contains three urns: u1, u2, u3. u1 contains 3 red and 2 yellow marbles. u2 contains 3 red and 7 yellow marbles. u3 contains 1 red and 4 yellow marbles. 66) referring to urns we enter the room and select an urn, but we are not sure which, and then we randomly remove a marble from the urn. find the probability that the marble is red.

Answer 1

Answer:

$\dfrac{11}{30}$

Step-by-step explanation:

Urn U1: 3 red and 2 yellow marbles, in total 5 marbles.

The probability to select red marble is $\dfrac{3}{5}=0.6.$

Urn U2: 3 red and 7 yellow marbles, in total 10 marbles.

The probability to select red marble is $\dfrac{3}{10}=0.3.$

Urn U1: 1 red and 4 yellow marbles, in total 5 marbles.

The probability to select red marble is $\dfrac{1}{5}=0.2.$

The probability to choose each urn is the same and is equal to $\frac{1}{3}.$

Thus, the probability that the marble is red is

$\dfrac{1}{3}\cdot 0.6+\dfrac{1}{3}\cdot 0.3+\dfrac{1}{3}\cdot 0.2=\dfrac{1.1}{3}=\dfrac{11}{30}.$