Information You roll two dice. If the sum is greater than 7, you lose the amount

Question

Information

You roll two dice.

If the sum is greater than 7, you lose the amount of the sum.

If the sum is less than 7, you earn the amount of sum.

If the sum is 7, you toss a coin. If the head comes out, you earn $20; otherwise, you get nothing.

Build a simulation model and run it 100,000 times.

Question 1 (1 point)

The first step is to simulate die 1. Which formula to use?

Question 1 options:

a.) =randbetween(1, 6)

b.) =randbetween(1,2)

c.) =if(rand()<0.25, 1, 2)

d.) =if(rand()<0.5, 1, 6)

Question 2 (1 point)

The second step is to simulate die 2. Which formula to use?

Question 2 options:

a.) =if(rand()<0.5, 1, 6)

b.) =if(rand()<0.25, 1, 2)

c.) =randbetween(1,2)

d.) =randbetween(1, 6)

Question 3 (1 point)

The third step is to calculate the sum of the two dice in B4. The fourth is to simulate the coin. Which formula to use for the fourth step?

Question 3 options:

a.) =randbetween(1, 6)

b.) =if(rand()<0.5, 1, 6)

c.) =randbetween(1,2)

d.) =if(rand()<0.25, 1, 2)

Question 4 (1 point)

The fifth step is to determine the payoff. Which formula to use?

Question 4 options:

a.) =IF(B4=7, 20, IF(B4<7, B6, -B6))

b.) =IF(B4>7, -B4,IF(B4<7, B4, IF(B6=1,20, 0)))

c.) =IF(B4>7, -B4,IF(B4<7, B6, IF(B6=1,20, 0)))

d.) =IF(B4<7, B4,IF(B4>7, -B4, IF(B6=2,20, 0)))

Question 5 (3 points)

After running the model (that is, the payoff) 100,000, answer the question. What is the average payoff? (Round your answer to four decimal places. For example, 1.2345)

Your Answer:

What is the chance of winning $20? (Answer in four decimal places. For example, 0.1234.)Question 6 (3 points)

Your Answer:

a.) =randbetween(1, 6)

b.) =randbetween(1,2)

c.) =if(rand()<0.25, 1, 2)

d.) =if(rand()<0.5, 1, 6)

Explanation / Answer

Q1) The number on the dice throw here is simulated using the EXCEL function:

= RANDBETWEEN(1, 6)

as each of the 6 numbers on the dice throw are equally likely from 1 to 6

Q2) Similar to the first dice, the second dice would also be simulated in exactly the same way as:

= RANDBETWEEN(1, 6)

as each of the 6 numbers on the dice throw are equally likely from 1 to 6

Q3) For the similation of the coin toss, we just have two outcomes - either Heads or Tails. Therefore we just have to simulate between 2 numbers 1 and 2.

=RANDBETWEEN(1,2)

Q4) We lose the sum on dice if the sum on dice is greater than 7 and win it if the sum of less than 7. This condition itself is only in one of the 4 options. This is represented as:

b.) =IF(B4>7, -B4,IF(B4<7, B4, IF(B6=1,20, 0)))

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