Question

Part A

List Marty’s sample space for three games of rock-paper-scissors. Use the abbreviations R for rock, P for paper, and S for scissors. For example, one possible outcome is paper-paper-paper, or P-P-P.Part B
Based on the list you created in part A, what is the size of the sample space?Part C
Suppose that Adrian chooses only rock or scissors during the three games. List Adrian’s sample space given this condition.Part D
Based on the list you created in part C, what is the size of Adrian’s sample space?Part E
Who has the larger sample space, and how much larger is it?

Answer 1

Explanation:

Marty’s sample space for three games:

P-P-P R-P-P S-P-P

P-P-R R-P-R S-P-R

P-P-S R-P-S S-P-S

P-R-S R-R-S S-R-S

P-R-R R-R-R S-R-R

P-R-P R-R-P S-R-P

P-S-R R-S-R S-S-R

P-S-S R-S-S S-S-S

P-S-P R-S-P S-S-P

Answer 2

Explanation:

Part A

Marty’s sample space for three games:

P-P-P R-P-P S-P-P

P-P-R R-P-R S-P-R

P-P-S R-P-S S-P-S

P-R-S R-R-S S-R-S

P-R-R R-R-R S-R-R

P-R-P R-R-P S-R-P

P-S-R R-S-R S-S-R

P-S-S R-S-S S-S-S

P-S-P R-S-P S-S-P

Part B

The size of the sample space is 27.

Part C

Adrian’s sample space for three games if he chooses only rock or scissors:

R-R-S S-R-S

R-R-R S-R-R

R-S-R S-S-R

R-S-S S-S-S

Part D

The size of Adrian’s sample space is 8.

Part E

The size of Marty’s sample space is 27, and the size of Adrian’s sample space is 8. Marty’s sample space is larger than Adrian’s. There are 19 (27 – 8 = 19) more outcomes in Marty’s sample space than in Adrian’s.