You and a friend decide to take a break from studying statistics and go to a cas

Question

You and a friend decide to take a break from studying statistics and go to a casino for some gambling. You decide to play a game in which you bet on whether a coin comes up heads or tails. You watch for a while before you play and see that four times in a row it comes up head. Your friend gets all excited and tells you to put all of your money on tails because the law of averages says that the coin is due for tails to come up. What do you say?

Your friend wants to know how unusual it is to get 3 heads in a row if you flip a coin 5 times. Use your calculator to simulate tossing a coin by going to Math>Prob>randomint(

Enter (0,1,5).

Choose either 0 or 1 represent heads.

Run the simulation 10 times and keep track of your results.

Create an experimental distribution.

Create a theoretical distribution.

Explanation / Answer

as law of averages tells that the coin is due for tails to come up. But as per probability distribution of head and tail, there is equal probability that head will come in further chances.

Here Pr(3 heads in a row if flip a coinf 5 times) = (1/2)3 = 1/8 = 0.125

Now we will simulate a random simulation for 10 times.

The results are

and we can see there are 3 heads in row too. Where tail = 0 and head = 1

Here theoreticla distribution is p(x) = BIN(X; 5; 0.5)

experimental distribution = X = 0 if tails ; X =1 if heads

Simulation 1 Simulation 2 Simulation 3 Simulation 4 Simulation 5 Simulation 6 Simulation 7 Simulation 8 Simulation 9 Simulation 10 1 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 Total Heads 2 4 3 2 2 4 2 2 2 4 Total tails 3 1 2 3 3 1 3 3 3 1

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