Question

Instructions:

1. Get 4 coins, any country, any value, as long as it is 2-sided with heads on one side and tails on the other.

2. Without actually flipping the coins, write down what you think would be the subjective probabilities of the following sequences:

A. P(THHT) B. P(TTTT) C. P(THTT)

A subjective probability is a probability measurement based on your opinion or judgment or historical facts or current events without conducting an experiment or using any mathematical theories for computing probability.

2. Perform an experiment of tossing the 4 coins 30 times, recording the sequence of your 30 outcomes in a spreadsheet/table, e.g.

Toss #: Sequence

1 : HTTH

2 :TTTT

... : ....

30 :HTHT

3. Based on your outcomes, determine the number of times you got the following sequences in your N= 30 tosses:

A. n(THHT) B. n(TTTT) C. n(THTT)

4. Using your answer in #3 and the formular P = n/N, compute the experimental (empirical) probabilities of the following sequences:

A. P(THHT) B. P(TTTT) C. P(THTT)

5. Construct a tree-diagram based on equally likely events for tossing one coin 4 times.

6. Based on your tree-diagram, compute the theoretical probability of the following sequences:

A. P(THHT) B. P(TTTT) C. P(THTT)

7. Create a spreadsheet/table that allows for ease in comparing your record of the subjective, experimental and theoretical probabilities for the three sequences, viz., THHT, TTTT, THTT. Is it okay for your subjective, experimental and theoretical values for each sequence to be equal or different. Justify your answer.

Answer 1

1. Suppose we take four unbiased coin, that is, the chance of coming head and tell from each coin are equal or

Let we flip them indepednetly. Thus

2. We got

1 T T T H 2 H T H T 3 T H H T 4 T T T T 5 T H H T 6 H T T T 7 H H H T 8 H H H T 9 T H H H 10 H H T H 11 H T T H 12 H T H T 13 T H H H 14 H T H T 15 T H T H 16 T T H H 17 H H T T 18 H H T H 19 T H H T 20 T H T H 21 H H H T 22 T T T H 23 H T H T 24 T T H H 25 T H H H 26 H T T T 27 H T H H 28 T H T T 29 T H T T 30 H T T T

Also we obtain

A. n(THHT)= 3 B. n(TTTT) = 1 C. n(THTT) =2

4.

5.

	SUBECTIVE	EXPERIMENTAL	THEORETICAL
THHT	1/16	1/10	1/16
TTTT	1/16	1/30	1/16
THTT	1/16	1/15	1/16

Here the experimental probablity is different because our sample size is small and our experiment is random. It may also be happen that we may not observe TTTT sequence. Also, It is not necessorery that all the three probablities are equal.