Question

Urn 1 contains 7 red balls and 3 black balls. Urn 2 contains 4 red balls and 1 black ball. Urn 3 contains 4 red balls and 3 black balls. If an urn is selected at random and a ball is drawn, find the probability that it will be red.

enter your answer as a decimal rounded to 3 decimal places

Answer 1

We have the following probabilities of selecting the 3 Urns:

P(Urn 1)=1/3
P(Urn 2)=1/3
P(Urn 3)=1/3

We have assigned equal probabilities by assuming that the probability of selecting each urn is equal.

Also the probability of selecting red ball from the 3 urns is given as:

P(Red/Urn 1)=7/10 Since the first urn contains total 10 balls (7red+3 black) therefore the probability
P(Red/Urn 2)=4/5 Since the second urn contains total 5 balls (4 red+1 black) therefore the probability
P(Red/Urn 3)=4/7 Since the third urn contains total 7 balls (4 red+3 black) therefore the probability

We need to calculate the probability of getting a red ball:

P(Red)=P(Urn 1)*P(Red/Urn 1)+P(Urn 2)*P(Red/Urn 2)+P(Urn 3)*P(Red/Urn 3)=(1/3)*(7/10)+(1/3)*(4/5)+(1/3)*(4/7)=0.6904