Probability with marbles

Question

Container A has 3 blue marbles and 2 purple marbles and Container B has 1 purple marble and 3 green marbles and 1 blue marble. An experiment consists of randomly selecting a marble from Container A and then selecting a marble from Container B. Use any effective method to find your answers. Express each answer as a fraction.Clearly show hour work .

a. What is the probability of selecting two marbles of the same color ?

b. What is the probability of selecting a purple and a green marble?

Answer 1

Our containers:   A = {3B, 2P}    B = {1P, 3G, 1B}

Probability of selecting two marbles of the same color.

  This occurs if you get 2 Blues OR if you get 2 Purples. For OR statements, you add the probabilities:

    P(B,B or P,P) = P(B,B) + P (P,P)

 Now to find P(B,B) and to find P(P,P): Since picking out of 2 different bags makes each pick an

independent event, to find the probability of 2 independent events happening, you just multiply the

probability of each independent event:

        P(B,B) = 3/5 * 1/5 = 3/25

        P(P,P) = 2/5 * 1/5 = 2/25

        P(B,B or P,P) = P(B,B) + P(P,P) = 3/25 + 2/25 = 5/25

Probability of selecting a purple and a green marble.

   

   This only happens if Purple is selected out of the first bag and then green out of the second bag.

   Since these events are independent, we again multiply the independent probabilities.

   P(P,G) = P(P) * P(G) = 2/5 * 3/5 = 6/25

           ( P(P) refers to the P (Purple from first bag).)