Transcript Theoretical vs. Experimental Probability

Bell Ringer
• Solve and combine like terms when possible.
7d + 3(d + 3) – d
8f2 – f(6 – f) + 10f + 12(f + 3)
Probability
Mr. Haupt
CC.2.1.8.E.1
Probability
• The probability of an event tells you how likely it is that
something will occur.
• It is written like this: P(event)
• So, the probability of getting tails when flipping a coin would be
written as P(tails)
Outcome
• The outcome is the result of a single trial.
• As in the roll of a dice, the flip of a coin, one pick out of a bag of
marbles, etc.
• Favorable outcome – the outcome we want to happen. If we
want to roll a 4 on a dice, then that is our favorable outcome.
Sample Space
• The list of all possible outcomes is called the sample space.
• If we are talking about rolling a dice, the sample space would
be 1,2,3,4,5,6
Event
• An event is any outcome or group of outcomes.
Example of how this works.
• Say we would want to find the probability of rolling an even
number on a dice.
• Event – Rolling an even number.
• Sample Space – 1,2,3,4,5,6
• Favorable Outcome – 2,4,6
• We will use this information to find the theoretical probability.
Theoretical Probability
• The theoretical probability in the easiest terms is: what
SHOULD happen.
• We can find the theoretical probability with this formula:
• P(event) = number of favorable outcomes
number of possible outcomes
• The theoretical probability of getting tails on a coin flip is .5 or
50%
• This does not mean that these will be your actual results.
Theoretical Probability Continued
• The probability of an event can be written as a fraction, a
decimal, or a percent. In terms of decimals, the range goes
from 0 to 1.
0
Impossible
Event
Ex: Rolling a
7 on a dice
0.5
Equally Likely
as not
Getting tails
when flipping coin
1
Certain
Event
Rolling less than
7 on a dice
Complement of an Event
• The complement of an event is all the outcomes not included
in the original event.
• So if we go back to rolling a dice, the possible outcomes are
1,2,3,4,5,6. If we look at rolling an even number 2,4,6, then
the complement to that event would be all the odd numbers
1,3,5.
Odds
• Sometimes we see probability in the form of odds, especially
in sports, gambling, etc.
• We use odds to compare favorable and unfavorable outcomes.
• The odds of flipping tails are 1 to 1, or 50/50.
• The odds of the Eagles winning the Super Bowl are 1 million to
1. (Actually it is 20 to 1 according to Vegas, but believe me, it
ain’t happening.)
Experimental Probability
• Experimental probability is what you actually get when you
perform the trials.
• We use the following formula to find it:
• P(event) = number of times the event occurs
number of times the experiment is done
• The theoretical probability of getting heads is 50%, but let’s
say you try it 20 times and get 12 heads and 8 tails, your
experimental probability is 60%.