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Cloud [144]
3 years ago
12

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 conta

ins 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.
Mathematics
1 answer:
Archy [21]3 years ago
4 0

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}.

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