Question

Suppose we have two urns, Urn 1 and Urn 2. Urn 1 contains 9 red marbles and 11 white marbles. Urn 2 contains 3 red marbles and 13 white marbles. The experiment consists of first choosing an urn with equally likely probability, and then drawing a marble from that urn. What is the probability of choosing Urn 1 and a white marble?

Answer 1

Answer: P (A) = 11/40

Step-by-step explanation: There are 2 urns in the experiment and they have equal probability of being chosen. So: P(1) = 1/2.

Inside Urn 1, there are a total of 20 marbles with 11 of them being white. So P(W) = 11/20

The probability of choosing Urn 1 and a white marble is:

P(A) = P(1)*P(W)

P(A) = $\frac{1}{2} . \frac{11}{20}$

P(A) = $\frac{11}{40}$

P(A) = 0.275

The probability of Urn 1 and white marble is 11/40 or 0.275.

Answer 2

Answer:

P(x1∩W) = 11/40 = 0.275

the probability of choosing Urn 1 and a white marble is 0.275.

Step-by-step explanation:

Let x1 and x2 represent each urn 1 and 2 respectively,

And R and W represent red and white marbles respectively.

the probability of choosing Urn 1 and a white marble is

P(x1∩W) = P(x1) × P(W in x1) ......1

Where;

P(x1∩W) = the probability of choosing Urn 1 and a white marble

P(x1) = probability of selecting urn 1

P(W in x1) = the probability of choosing white marble in urn1

Since the two urn are of equal probabilities, the probability of choosing urn 1 is half;

P(x1) = 1/2

For urn 1;

Red marbles = 9

White marbles = 11

Total = 20

P(W in urn1) = 11/20

From equation 1;

P(x1∩W) = 1/2 × 11/20 = 11/40

P(x1∩W) = 11/40 = 0.275

the probability of choosing Urn 1 and a white marble is 0.275.