Question

For Exercises explain how each experiment can be simulated by using random numbers.

Two players match pennies.

Answer 1

It is given that two players are playing the match the pennies game.

The game can be described as follows:

 

Both the players (A&B) toss coins. If both get Heads or if both get Tails, then the result is “Match”. If both the players get different outcomes, then the result is “Non-Match”. We need to create a simulation to represent this situation.

 

Step1: We first list the possible outcomes.

The results of the game can be divided into two categories based on the status of the outcome. They are either match or mismatch.

 

Step2: Assign the probabilities to each outcome.

The number of outcomes in “two-coins tossing experiment” is 4. Of these outcomes, two outcomes HH, TT are favorable to event “Match” and the other two HT and TH are favorable to “Non-Match”.

Therefore, P (match) = 0.5, P (non-match) = 0.5.

 

Step3: Set up a correspondence between the random numbers and the outcome.

Use random numbers 0 to 9. The even digits represent a match and odd digits represent a non-match.

 

Step4: Select random number from table and categorize based on the classification given

in the previous step. That is, if the random number is one among 0, 2, 4, 6, 8, then the result of the game is “Match”. Otherwise, the result is “non-match”.

 

Step5: Continue the procedure until we get the required number of trials

The results of the simulated experiment are as follows:

Outcome	Result	Outcome	Result	Outcome	Result	Outcome	Result	Outcome	Result
6	M	7	N	5	N	4	M	3	N
0	M	8	M	2	M	5	N	4	M
1	N	8	M	6	M	2	M	6	M
5	N	3	N	5	N	5	N	6	M
6	M	1	N	0	M	7	N	3	N
7	N	6	M	5	N	7	N	2	M
0	M	4	M	3	N	6	M	7	N
6	M	5	N	1	N	7	N	1	N
3	N	6	M	2	M	0	M	8	M
4	M	9	N	6	M	0	M	2	M

 

From the above results, we can say that there exist 27 Matched games and 23 Non-Matched games.

From the above results, we can say that there exist 27 Matched games and 23 Non-Matched games.