We have two urns. the first urn contains two balls labeled 1 and 2. the second urn contains three balls labeled 3, 4, and 5. we choose one of the two urns at random with equal probability and then sample one ball, uniformly at random, from the chosen urn. what is the probability that we picked the ball labeled 5

The probability of randomly picking a ball labeled 5 from the urn is 1/6

Recall :

Number of urns = 2

Probability of selecting urn 2 :

Ball labels in urn 2 = 3, 4, 5

Probability of picking a ball labeled 5 from urn 2 :

Therefore, the probability of selecting a ball labeled 5 is :

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The probability of picking the urn with the number 5 in it is 1 out of 2, which is written as 1/2.

The probability if picking the number 5 out of that urn would be 1 out of 3 , written as 1/3.

The probability of both is found by multiplying the two probabilities together:

1/2 x 1/5 = 1/10 probability.

the answer is 62.8 cubic units