In the game of craps, people bet on the outcome of the throw of two, six-sided d

Question

In the game of craps, people bet on the outcome of the throw of two, six-sided dice. Specifically, wagers are placed on the sum of the outcome on the upward facing number on each of the two dice. We are going to discuss relative likelihoods by counting the number of ways (the number of microstates) associated with specific sums (the macrostate).

(a.) How many microstates are associated with a throw summing to 4?

(b.) How many microstates are associated with a throw summing to 5?

(c.) How many microstates are associated with a throw summing to 10?  

(d.) Which is more likely, rolling 2 dice that sum up to 4 or rolling 2 dice that sum up to 5?

The first event is more likely. The second event is more likely. Both events are equally likely.  

(e.) Which is more likely, rolling 2 dice that sum up to 4 or rolling 2 dice that sum up to 10?

The first event is more likely. The second event is more likely. Both events are equally likely.

Explanation / Answer

a) If we name the dice A and B respectively, we can get a sum of four if either die A=1 and die B=3, die A=2 and die B=2 or die A=3 and die B=1.

So in this case we have 3 microstates, which can be represented as (1,3) (2,2) (3,1)

b)In this case we have 4 microstates, they are (1,4) (2,3) (3,2) (4,1)

c)In this case we have 3 microstates, they are ](6,4) (5,5) (4,6)

d) Since the number of microstates associated with a throw summing to 5 (4) is greater than the number of microstates associated with throw summing to 4 (3)

Then a throw summing to 5 is more likely than a throw summing to 4

Answer: The second event is more likely

e) Since the number of microstates is the same (3) for both macrostates

Then, both events are equally likely

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.