Question

You are presented with three urns. each urn has 10 marbles. in addition, each urn holds only black or red marbles. urn 1 has 3 red marbles. urn 2 has 8 red marbles. urn 3 has 5 red marbles. you randomly pick 1 marble from 1 of the three urns. calculate the probability that it is a black marble.

Answer 1

To calculate this probability we must take into account that there is the same probability that any of the 3 urns is chosen.
 This probability is:
 P (U1) = P (U2) = P (U3) = 1/3
 Urn 1 contains 7 black and 3 red marbles
 Urn 2 contains 2 black and 8 marbles network
 Urn 3 contains 5 black marbles and 5 red marbles.

 The probability of obtaining a black marble in Urn 1 is 7/10.
 The probability of obtaining a black marble in Urn 2 is 2/10
 The probability of obtaining a black marble in Urn 3 is 5/10.

 Then we look for the probability of obtaining a black marble from urn 1 or a black marble from urn 2 or a black marble from urn 3. This is:
 P (U1yB) + P (U2yB) + P (U3yB)
 So:
 (1/3) * (7/10) + (1/3) * (2/10) + (1/3) * (5/10) = 0,2333 + 0,0667 + 0,1667 = 0, 4667.
 The probability that it is a black marble is 46.67%