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# Probability

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by

## Kayla Krar

on 4 December 2013

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#### Transcript of Probability

Probability
Odds
# of desirable outcomes
# of possible outcomes
Probability and Odds
Out of 100 days with the same specific weather conditions, it rained on 50 days.
= 50/100
= 1/2 or 50%
Desirable outcomes : undesirable outcomes
Desirable outcomes
Possible outcomes
In a group of 30 people,
12 have blue eyes. What are the odds of selecting someone with blue eyes?
12 blue : 18 other
12:18 or 6:9
= 40%
# of desirable outcomes:
# of undesirable outcomes*
Note: when using a ratio, both numbers combined equal the total.
(Before being reduced)
Both describe the likelihood of an event
How do they relate?
There are 17 marbles in a bag. Of these marbles, there are 4
blue
, 6
yellow
, 2
red
, and 5
green
.

What is the probability a
yellow
marble will be picked? What are the odds?
There are 18 marbles in a bag. Of these marbles, there are 4
blue
, 6
yellow
, 3
red
, and 5
green
.

What is the probability a
yellow
marble will be picked? What are the odds?
Probability: (success/total)
6 in 18 (1/3 or 33.3%)

Odds: (success:failure)
6 to 12 (1:2)
This means there is a 50% probability of rain on a day with the same weather conditions.

The extent to which something is likely to happen or be the case.
What's the Difference?

The probability that a random day is Friday is 1/7,
but the odds of it being Friday are 1:6 .
Note: Probability cannot be a negative number.
nPr Permutation
"Probability" involves positive outcomes within the total outcomes

"Odds" compares the positive outcomes with the negative outcomes
The number of possible combinations that can be made without any being repeated.
nCr Combinations
The amount of possible combinations that can be made
(the ORDER of the combinations do not matter)
How is it calculated?
Calculating Probability of Multiple Random Events
Step 1: Break the problem into parts.

Step 2: Multiply the probability of each event by the other.

Step 3: Reduce if necessary.

This would give us the probability of multiple events occurring one after another.
Steve has two dice (standard, six-sided). What is the probability that he will roll a pair of 5's?
Step 1: We know that the probability of rolling a "five" is 1 in 6.

Step 2: He is rolling two dice, so we multiply the first probability with the second.
Note: The order of the combinations does matter when considering repetition.
nPr Permutation
*to find the amount of undesirable outcomes, subtract the desired outcomes from the total outcomes
Note: Each roll is an independent event.

(What you roll with the first die does not affect what happens with the second.)
1

6
x
1

6
=
1

36

1/36 is 2.7% therefore rolling a pair of fives 2.7% .
How many combinations are possible for 10 people sitting in 4 chairs?
nPr = n!/(n-r)!
10P4 = 10!/(10-4)!
= 5040
Note: Each roll is an independent event.

(What you roll the first time does not affect what happens the second.)
There are 5040 possible combination of 10 people sitting in 4 chairs
In a study, 4 people are chosen at random
from a group of 10 people.
How many different groups can be made?
nCr = n!/(n-r)!r!
10C4 = 10!/(10-4)!4!
= 210

Therefore, 210 different groups of people can be chosen.
The ratio of the likelihood of an event's occurrence to the likelihood of it not occurring
There is a button on your calculator for this.
Don't freak out!
nCr Combination
Try it yourself!
In a game of rock, paper, scissors versus one other person;

What is the probability you will win?
What are the odds?

What about against two other people?
Try it out
Playing against one opponent, what is the probability you will win RPSLS?
Rock, paper, scissors, lizard, spock
Note:
For each of the 5 choices, there are two possible wins, one tie, and two losses.