Question

We have two urns. The rst urn contains two balls labeled 1 and 2. The second urn contains three balls labeled 3, 4 and 5. We choose one of the 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?

Answer 1

The probability of picking the ball labeled 5 is calculated by first determining the chance of selecting the urn containing ball 5 (50%) and then the chance of picking ball 5 from that urn (33.33%). Multiplying these chances gives us an overall probability of about 16.67%.

Step-by-step explanation:

Calculating the Probability of Picking the Ball Labeled 5

The process of determining the probability involves two steps: first, selecting an urn, and second, picking a ball from the chosen urn. Since we choose between two urns randomly and with equal probability, each urn has a 50% chance to be selected.

The first urn is irrelevant to the event of picking ball number 5 since it does not contain this ball. Therefore, we only focus on the second urn, which contains three balls, including the one labeled 5. The probability of picking ball number 5 from the second urn, provided that this urn is chosen, is 1 out of 3 or approximately 33.33%.

Now, the combined probability of first choosing the second urn and then picking ball number 5 can be found by multiplying the probabilities of these independent events:

• Probability of selecting the second urn: 1/2
• Probability of picking ball 5 from the second urn: 1/3

Thus, the overall probability of picking ball number 5 is:

1/2 × 1/3 = 1/6 (about 16.67%)

Answer 2

Answer:0.1667

Step-by-step explanation:

Given

we have two urns labelled let say A and B

Urn A has balls labelled as 1 and 2

Urn B has balls labelled as 3,4 and 5

Probability of picking the number 5 ball
`=Probability\ to\ choose\ Urn\ B* Probability\ to\ choose\ no\ 5 ball`

Probability to choose Urn B
`=(1)/(2)`

Probability to choose no 5 ball from Urn B
`=(1)/(3)`

Required Probability
`=(1)/(2)* (1)/(3)=0.166`