ZOOL 304, Evolution

Results from probability homework exercise
January 31, 2003

We gathered data from 2000 coin flips 756 dice rolls.

The overall results came close to the expected values but (also as expected) not exactly the expected values.
Expected
Actual
Heads (2000 flips)
1000
997
Tails (2000 flips)
1000
1003
Dice #1 (756 rolls)
126
118
Dice #3 or #5 (756 rolls)
252
261

 

For 20 flips of a coin, the most likely individual result is10 heads.  For 200 flips of a coin, the most likely individual result is100 heads.  However, as the data you gathered indicates, this most likely result is in fact rather unlikely.  (No other particular result is more likely, but the sum of the probabilities of all the other possibilities is rather large.)

 

For 20 flips, difference from expected result (10 heads)

0
1
2
3
4
5
6
7
8
9
Number of instances, out of 100 trials
16
27
24
14
10
6
3
0
0
0

 
Individual results

For 200 flips, difference from expected result (100 heads)

1
2
2
3
5
7
9
14
16
24

 
For 36 rolls of a die, the most likely result is 6 rolls of number 1 (or any other number), or 12 rolls of either number from a particular pair of numbers.  Again, as the data you gathered indicates, this most likely result is in fact rather unlikely.  

 

For 36 rolls, difference from expected result (6 rolls of number 1)

0
1
2
3
4
5
6
7
8
9
Number of instances, out of 21 trials
6
9
2
1
2
1
0
0
0
0
 

For 36 rolls, difference from expected result (12 rolls of numbers 3 or 5)

0
1
2
3
4
5
6
7
8
9
Number of instances, out of 21 trials
2
10
3
3
1
0
1
0
0
0

 

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SIUC / College of Science / Zoology / Faculty / David King / ZOOL 304
URL: http://www.science.siu.edu/zoology/king/304/coinflip.htm
Last updated:  1 February 2003 / dgk