Slides for part I
Ques%on 1
You toss a fair coin repeatedly. Fair means, that each 7me you toss the coin, the chance of it landing heads (H) is the same as the chance of it landing tails (T). Which pa<ern do you think is more likely? (Circle your answer.)
HHHH HHHT No difference
Which pa<ern do you think is more likely? HHHH HHHT No difference
Why?
Answer:
All outcomes are equally likely with probability 1/16 each
Ques%on 2
You are given a non-­‐transparent box containing a large number of iden7cal marbles, half are black (B) and half are white (W). Take out a marble and note its colour. Put it back and give the box a li<le shake. Take out another marble and note its colour. Do this repeatedly. Write down a colour sequence (B or W) of 10 marbles you might have observed.
What is the first one?
Classroom vote...
Results from classroom experiments
7 lecture classes with first and second year UG students,
between 39 and 268 students totalling 857 students.
About 90% of the students picked Black first!
How many alternations do you have?
Alternation means going from B to W or from W to B
Classroom vote...
What is the probability for an alternation?
Alterna7on means BW or WB. Possible outcomes for pairs are WW, WB, BW, BB. All are equally likely with probability 1/4 each.
P(alterna7on) = P(BW or WB) = P(BW) + P(WB) = 1/4 + 1/4 = 1/2
What is the probability for an alternation?
Alterna7on means BW or WB. Possible outcomes for pairs are WW, WB, BW, BB. All are equally likely with probability 1/4 each.
P(alterna7on) = P(BW or WB) = P(BW) + P(WB) = 1/4 + 1/4 = 1/2
How many alternations do you expect in
a sequence of 10?
On average, 4.5. Because there are 9 transi7ons, each with a probability of 1/2 to be an alterna7on.
Results from classroom experiments
7 lecture classes with first and second year UG students,
between 39 and 268 students totalling 857 students.
Students averaged about 5.
Humanities students (English, History): average about 5.5
Maths/Stats/Philosopy students: average about 4.5
t
100 black & white dots
Describe the patterns
100 black & white dots
Describe the patterns
constant
regular (alternating, periodic)
regular with random perturbations
66 colour changes
student generated fair coin flips
46 colour changes
computer generated fair coin flips
In this example, the computer generated sequence is more typical
for a fair coin tosses than the student generated one in the sense of
showing a number of alternations closer to the expected number of
49.5 alternations.