PROBABILITY

Also see Fractions, Decimals and Percent.

Kahn Academy Topic Videos:
https://www.khanacademy.org/math/ap-statistics/probability-ap#probability-multiplication-rule


PROBABILITY is a Mathematical Model used to predict future outcomes (EVENTS) based on prior (or expected) results.
CHANCE is a Random Activity or event (Not predictable).

Probability is most oven expressed as a Decimal between ZERO (0) never happen and ONE (1) certainly will happen.  A .5 or 1/2 probability is an event is equally likely or unlikely (50/50).

Decimals may also be expressed as a fraction: (Event / Total Outcomes)
Decimals can also be expressed as PERCENT:
1/2 = .5 = 50%

Theoretical Probability is that given a "FAIR" or "UNBIASED" tool, the outcomes can be predicted.
There are 2 sides to a Coin: The probability of getting: Heads or Tails is "1/2".

There are 6 sides on a Die: the probability of getting any number is: "1/6"
The probability of rolling an EVEN P(2, 4, 6) is 3/6 or 1/2 or .5 or 50%
The probability of rolling an ODD P(1, 3, 5) is 3/6 or 1/2 or .5 or 50%
The Probability of a rolling a ZERO or a number Greater than 6 is ZERO (Impossible)
The Probability of rolling a number Greater Than 4: (5 or 6) = 1/6 + 1/6 = 2/6 = 1/3 or 33%

There are 52 cards in a DECK: The probability of getting an ACE is "4 out of 52" or 4/52 = 1/13 = .0769 or 7.69%

Experimental Probability Based on an "Experiment" to predict the future based on the past outcomes.
The greater number of "SAMPLES" taken and the larger the sample is to the actual population; the closer the results of your experiment should approximate the Theoretical Probability.
If you "toss" a fair coin 10 times it is possible for it to be HEADS all ten times (but very unlikely)!

Tossing 1 coin 10 times or tossing 10 coins 1 time have the same probability of outcomes for total heads and tails.

COMPOUND Probability is when the Probability of one event depends on the probability of a prior event.
What is the probability of getting 2 heads in a row?
The Probability of the FIRST Head is 1/2.
The Probability of a SECOND Head is also 1/2.
But the probability of getting TWO heads is: 1/2 x 1/2 = 1/4
4 OUTCOMES:   (Head & Head),  (Head & Tail),  (Tail & Head),  (Tail & Tail)

Sometimes the COMPOUND Probability is based on MULTIPLE outcomes happening. Then you ADD the probability of each event:

You might also be asked for the PROBABILITY OF AN EVENT (NOT TO HAPPEN).
What is the probability of not getting a head if you flip a coin two times:
HH, HT, TH TT.  There are 4 outcomes of filling 2 coins.   Three outcomes have heads or only 1 does not have a head: 1/4 = .25 or 25%

ODDS are another way to express probability but the ratio is
GOOD / BAD or Winning / Losing

SPINNER Simulation Use this on-line Spinner with various defaults (or customize it) for Experimental Probability.

Link to PROBABILITY GAMES
​
Sample Simulation Experimental OUTCOME With Spinners: Experimental Spinners
An Experiment With 1 Die
An Experiment With 2 Dice

Probability Quiz

BLOOD TYPE DISTRIBUTION:
https://en.wikipedia.org/wiki/Blood_type_distribution_by_country


Worksheets:
https://www.easyteacherworksheets.com/math/stats-compoundprobability.html

Revised: April 24, 2024