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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 :

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 [tex]=Probability\ to\ choose\ Urn\ B\times Probability\ to\ choose\ no\ 5 ball[/tex]

Probability to choose Urn B[tex]=\frac{1}{2}[/tex]

Probability to choose no 5 ball from Urn B[tex]=\frac{1}{3}[/tex]

Required Probability[tex]=\frac{1}{2}\times \frac{1}{3}=0.166[/tex]

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