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

Question

Two marbles are drawn at random and without replacement from a box containing three blue marbles and four red marbles. a. List the sample points for this experiment Choose the correct answer below. Denote the marbles as B1, Bo, Ba, R1, R2, R3, and R4 O A. B1, B2, B3, R1, R2, R3, R4 O B. (B1, B2) (B1,B3) (B2, B3) (B1, R1) (B1, R2) (B1, R3 (B1, R4) (B2, R1) (B2 R2) (B2,R3) (B2,R4)(B3 R1) (B3 R2) (B3 R3)(B3, R4) (R1, R2) (R1, R30 (R1,R4) (R2,R30 (R2, R4) (R3,R4) O C. (B1,R1) (B1,R2) (B1,R3) (B1,R4) (B2,R1) (B2,R2) (B2,R3) (B2,R4) (B3,R1) (B3,R2) (B3,R3) (B3,R4) b. Assign probabilities to the sample points. Choose the correct answer for the probabilities associated with the sample points found in the previous step O A. Each sample point has a probability of 21 O B. Each sample point has a probability of 12 O C. Each sample point has a probability of 5. O D. Each sample point has a probability of 1.

Explanation / Answer

a. Two marbles drawn from a total of 7 marbles so N(S)=C(7,2)=21

So answer is b.

b. As there are 21 sample probability of each sample is 1/21 so answer is A.

c. A. there are 3 ways in which 2 blue marbles drawn so P(A)=3/21=1/7

B. there are 12 ways in which one red and one blue marbles selected so required probability is 12/21=4/7

C. now there are 6 ways in which both red marbles so required probability is 6/21=2/7

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