**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.

Answer:

Probability is 2/5, or 20%.