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Quantitative Reasoning & Problem Solving
120 © 2014 Pacific Crest
3. In flipping a coin three times what are the likelihoods of getting 3 heads, 2 heads and 1 tail (in that
order), 1 head and 2 tails (in that order), or 3 tails?
4. What is an easy way to calculate combinations (say 3 heads, 2 tails) in flipping a coin five times?
Mathematical Language Terms and notation
count — the number of occurrences of a specific outcome
event — subset of the sample space
independence — each event has no impact or influence on the probability of any other event
likelihood — probable chances of an occurrence of an event
measure of likelihood
very rare rare unlikely possible likely very likely certain
less than 0.1% 0.1% to 1% 1% to 5% 5% to 25% 25% to 50% 50% to 99% greater than 99%
outcome — a possible result of the experiment
sample space — a complete set of all possible outcomes
trial — the action taken that produces an event
Information What you need to know
Readings Resources
Methodology Determining the Likelihood of an
Event for Independent Trials
Scenario:You flip a coin 10 times, getting 4 heads and 6 tails
Step Explanation Watch it Work!
1. Define the
experiment
Identify the trial and the number of
the trials
Trial: Flipping a coin
Number: 10 times
2. Outcomes of a
trial
Define the set of possible results of a
single trial and their likelihoods
Possible results: Heads or Tails
Likelihood: 50% each
3. Outcomes in the
sample space
Determine the unique outcomes
(sample space) of the experiment
There are 210 possible sequences
of heads/tails in the sample space
(1024 sequences)
4. Define the event Decide on which outcomes are of
interest in the experiment
Result of 4 heads and 6 tails
5. Outcomes in the
event
Count the number of outcomes in the
sample space for the defined event
Use Combinations: choosing 4
heads from 10 trials
C(10,4) = 210