Question

a) Three fair dice are tossed 1000 times.

Create a simulation of these 1000 tosses, and compute the probability that the sum of the three dice 7 or less. (Hint: randbtween)

b) Mike and Monica arrive randomly at the golf course between 8am and 10am.

What is the probability they arrive within 30min of each other? (Hint: 120*rand() ?)

Answer 1

a) Each die can roll 1 through 6 with equal probability. We will use =RANDBETWEEN(1,6) to generate integers from discrete uniform distribution in the  interval (1,6)

the probability that the sum of the three dice 7 or less is (number of simulation trials with sum 7 or less)/1000

Prepare this sheet

get this

ans: the probability that the sum of the three dice 7 or less is 0.154

Note: Paste as values to avoid changes

b) Mike and Monica arrive randomly at the golf course between 8am and 10am. There are 120 minutes between 8 and 10 AM. We just want to know how many minutes elapsed since 8 AM when each of them arrive.

Let X indicate the minutes elapsed since 8 AM when Mike and Monica arrive at the golf course. We know that X is uniformly distributed in the interval 0 to 120 minutes. We will simulate the time elapsed since 8 AM using 120*rand()

Note: To generate a continuous uniform random number in the interval (a,b), we use a+(b-a)*rand(). Here a=0 and b=120

We get the absolute value of the difference between the arrival of Mike and arrival of Monica after 8 AM.

the probability they arrive within 30min of each other is (Number of times in the simulation the absolute difference is 30 or less)/1000

Prepare the following

get this

ans: the probability they arrive within 30min of each other is 0.435

Note: Paste as values to avoid changes