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

`(11)/(30)`

Explanation:

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

The probability to select red marble is
`(3)/(5)=0.6.`

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

The probability to select red marble is
`(3)/(10)=0.3.`

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

The probability to select red marble is
`(1)/(5)=0.2.`

The probability to choose each urn is the same and is equal to
`(1)/(3).`

Thus, the probability that the marble is red is

`(1)/(3)\cdot 0.6+(1)/(3)\cdot 0.3+(1)/(3)\cdot 0.2=(1.1)/(3)=(11)/(30).`