Question

2. Urn 1 contains 5 white balls and 7 black balls. Urn 2 contains 3 whites and 12 black. A fair coin is flipped; if it is heads, a ball is drawn from urn 1, and if it is tails, a ball is drawn from urn 2. Suppose that this experiment is done and you learn that a white ball was selected. What is the probability that this ball was in fact taken from urn 2? (i.E., that the coin flip was tails)

Answer 1

Step-by-step explanation:

2. Urn 1 contains 5 white balls and 7 black balls. Urn 2 contains 3 whites ... A fair coin is flipped; if it is heads, a ball is drawn from urn 1, and if it is tails, ...

Answer 2

Answer:

THE RREQUIRED PROBABILITY IS = 12/37

Step-by-step explanation:

In order to get the probability,

Let the event be "T" such that when the coin flip is "tails".

and let the event be "W" when we select a white ball

Now according to the question :

P(W|T) = 3/15

and the P(W|T') = 5/12

As, the coin is a fair one , it is known to us that : P(T) = P(T') = 1/2.

Hence, the required probability,

P(T|W) = P(T∩W) / P(W)

= (P(W|T) . P(T)) / ((P(W|T) . P(T) + P(W|T') . P(T'))

= ((3/15).(1/2)) / ((3/15).(1/2) + (5/12).(1/2)) = 12/37

#SPJ3