4.2
Probability Models
probability model
- a description of a random phenomenon in the language of
mathematics
the description of a random variable has two components:
a list of possible outcomes
a probability for each outcome
The sample space S
of a random phenomenon is the set of all possible outcomes.
random phenomenon→ toss a coin
S= {H, T}
random phenomenon→ let your pencil fall blindly into table of random digits
S= {0, 1, 2, 3, 4, 5 ,6, 7, 8, 9}
random phenomenon→ toss a coin four times and record the results
vague- what constitutes an outcome?
random phenomenon→ toss a coin four times and record the results of each of 4 tosses in
order
S= {HHHH, HHHT, HHTH, HTHH, THHH…}
16 possibilities
random phenomenon→ toss a coin four times and count the number of heads
S= {0, 1, 2, 3, 4}
random phenomenon→ computer generates random number between 0 and 1
S= {all numbers between 0 and 1}
event
- an outcome or a set of outcomes of a random phenomenon (an event is a subset of
the sample space)
random phenomenon→ toss a coin four times and record the results of each of 4 tosses in
order
event A= “get exactly 2 heads”
event A expressed as a set of outcomes:
A= {HHTT, HTHT, HTTH, THHT, THTH, TTHH}