Question

For Exercises use random numbers to simulate the experiments. The number in parentheses is the number of times the experiment should be done.

Two coins are tossed. Find the average number of times two tails will appear. (40) 

Answer 1

From the given information, two coins are tossed we have to find the average number of times two tails will appear.

Here two coins are tossed, the possible outcomes are {HH, HT, TH, TT}.

 

Step 1: List of all possible outcomes. They are HH, HT, TH, TT.

Step 2: Assign the probabilities. Each outcome has a probability of 1/4.

Step 3: We need to find the number of times two tails will appear, for our convenience we denote ‘1’ for the occurring of outcomes of two tails and ‘0’ for the rest of the outcomes.

Step 4: Now, the probabilities are changed as 1/4 and 3/4. The probability for the outcome of two tails is 1/4. The probability for the rest of the outcomes is 3/4.

Step 5: By using MINITAB generate a random numbers 0 and 1. We get the following output.

Generate	Generate
0	1
0	1
0	0
1	1
1	1
1	1
0	0
1	0
1	1
0	1
1	0
1	0
0	0
1	0
1	1
0	0
0	0
0	1
1	0
0	0

Step 6: Count Number of ‘1’s in the above table.

 

Number of two tails occur = Number of ones in the table

                                               = 19

 

Average number of times two tails = 19/40.

                                                              = 0.475