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?

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.

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step-by-step explanation: