Two marbles are drawn at random and without replacement from a box containing tw

Question

Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles. a. List the sample points for this experiment. Choose the correct answer below. Denote the marbles as B_1, B_2, R_1, R_2, and R_3. A. B_1, B_2, R_1, R_2, R_3 B. (B_1, R_1) (B_1, R_2) (B_1, R_3) (B_2, R_1) (B_2, R_2) (B_2, R_3) C. (B_1, B_2) (B_1, R_1) (B_1, R_2) (B_1, R_3) (B_2, R_1) (B_2, R_2) (B_2, R_3) (R_1, R_2) (R_1, R_3) (R_2, R_3) b. Assign probabilities to the sample points. Choose the correct answer for the probabilities associated with the sample points found in the previous step. A. Each sample point has a probability of 1/5. B. Each sample point has a probability of 1/10. C. Each sample point has a probability of 1/6. D. Each sample point has a probability of 1. c. Determine the probability of observing each of the following events. A: {Two blue marbles are drawn} B: {A red and a blue marble are drawn} C: {Two red marbles are drawn} P(A) = (Type an integer or a simplified fraction.) P(B) = (Type an integer or a simplified fraction.) P(C) = (Type an integer or a simplified fraction.)

Explanation / Answer

Ans:

a)Option C is correct.

b)Option B is correct.

c)Probability that two blue marbles are drawn

P(A)=(2/5)*(1/4)=2/20=0.1

Probability that a red and a blue marble is drawn

P(B)=(2/5)*(3/4)=6/20=3/10=0.3

Probability that two red marbles are drawn

P(C)=(3/5)*(2/4)=0.6*0.5=0.3

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