3 Ihave three bags that each contain 100 marbles i Bag 1 has

3. Ihave three bags that each contain 100 marbles: i. Bag 1 has 75 red and 25 blue marbles; ii. Bag 2 has 60 red and 40 blue marbles; iii. Bag 3 has 45 red and 55 blue marbles. I choose one of the bags at random and then pick a marble from the chosen bag, also at random. a. What is the probability that the chosen marble is red? b. What is the probability that the chosen marble is a red marble from Bag 2? c. Given that the chosen marble is red, what is the probability that it came from Bag 2?

Solution

Sol(A)

75+60+45 red balls in 3 bags=180

total 300 bags

P(choosen marble is red)=180C1/300C1=180/300=0.6

SolutionB:

P(chosen marble red from bag2)=(60C1/100C1)=60/100=0.6

SolutionC:

P( selecting a bag)=1/3

P(chosen marble red from bag2)=1/3*60C1/100C1=60/300=0.2