Question

Flip a coin 10 times and record the observed number of heads and tails. For example, with 10 flips one might get 6 heads and 4 tails. Now, flip the coin another 20 times (so 30 times in total) and again, record the observed number of heads and tails. Finally, flip the coin another 70 times (so 100 times in total) and record your results again. We would expect that the distribution of heads and tails to be 50/50. How far away from 50/50 are you for each of your three samples? Reflect upon why might this happen? In response to your peers, comment on the similarities and differences between yours and your classmate’s data analyses. In particular, compare how far away you and your classmate are from 50/50 for each of your three samples.

Answer 1

Theoretical probability = 50%

Experimental probability varies.

See below for explanation.

Explanation:

This is a problem on theoretical and experimental probability. The results obtained would enable you understand their differences.

The theoretical probability is the result that is expected to happen, but it isn't always what eventually happens.

The theoretical probability of a coin landing on heads is ½ or 50%. This is same for tails.

The experimental probability is the probability obtained from carrying out the experiment. As this is the result of what actually happens, the experimental probability could be lesser or greater than or equal to 50%.

You are required to carry out the experiment. This is because the result would vary from person to person as well as from one experiment to the other.

First, make a table for the number of trials, outcome (head and tail each) and the frequency. Pen down the result for each of the experiment carried out. You can use a tally to make it easy for compilation.

See attachment for table.

Theoretical probability of 10 trials:

Head= 5, tail = 5

Theoretical probability of 30 trials:

Head= 15, tail = 15

Theoretical probability of 100 trials:

Head= 50, tail = 50

It all amount to 50% each

So do your experiment and record the results. Afterwards compare your result which is the experimental probability

for head and tail with the theoretical theoretical.

Also compare your result with that of your classmate.