Question

One urn contains one blue ball (labeled b1) and three red balls (labeled r1, r2, and r3). a second urn contains two red balls (r4 and r5) and two blue balls (b2 and b3). an experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. what is the total number of outcomes of this experiment?

Answer 1

12 outcomes

Explanation:

Given:-

Urn 1 : 1 blue ball & 3 red balls

Urn 2 : 2 blue & red balls.

Find:-

One of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. what is the total number of outcomes of this experiment?

Solution:-

- The number of possible outcomes when selecting one of the 2 urns available is = 2, since we can either choose Urn 1 or Urn 2.

- Once the urn is selected each urn has a total of 4 balls ( Red & Blue ). We are to choose 2 balls from the chosen urn. The number of combinations for selecting 2 out of 4 available is = 4C2 = 6 possibilities.

- Then the total number of combinations are:

Total outcomes = 2 * 6 = 12 outcomes

Answer 2

12 possibilities

Explanation:

In the first urn, we have 4 balls, and all of them are different, as they have different labels, so the group of two red balls r1 and r2 is different from the group of red balls r2 and r3.

The same thing occurs in the second urn, as all balls have different labels.

The problem is a combination problem (the group r1 and r2 is the same group r2 and r1).

For the first urn, we have a combination of 4 choose 2:

C(4,2) = 4!/2!*2! = 4*3*2/2*2 = 2*3 = 6 possibilities

For the second urn, we also have a combination of 4 choose 2, so 6 possibilities.

In total we have 6 + 6 = 12 possibilities.