Chapter 5, Section 6: Probability & Odds

Some Definitions to Keep in Mind

• OUTCOMES…are the possible results of an action.

• an EVENT is any outcome OR group of outcomes.

Ex: in rolling two dice, rolling a sum of 4 is an event corresponding two three different outcomes.

Randomness

• If its random,

if you can’t predict what is going to happen out of all of the possible outcomes,

then any outcome is EQUALLY LIKELY to occur.

Probability of an Event

• When outcomes are equally likely, you can use a RATIO to find the PROBABILITY OF AN EVENT.

• Probability of an Event = P(event) = Number of favorable outcomes/number of possible outcomes

Here is an Example:

• Find P(rolling an even number) with one dice.

1st: how many favorable out comes are there?

2nd: how many possible outcomes?

3rd: make a ratio.

P(rolling an even number) = 3/6 or ½.

Try These: Using a Standard Dice

• P(odd number):

• P(2):

• P(5 or 6):

1/2

1/6

1/3

0 to 1 in any Probability

• All probabilities range from zero to one.

• Kinda like decimals and fractions and ratios.

PROBABILITY

0.5, ½, 1:2

Equally likely as unlikely

More likelyLess likely

Certain EventImpossible Event

Complement

• The COMPLEMENT of an event is the OPPOSITE of that event.

• Example: P(rolling an even number), the complement would be P(rolling an odd number).

• So, the probability of an event, plus the probability of its complement, ALWAYS EQUALS 1.

Double Trouble• In the United States, the probability that a

child is a twin is 2 in 90, or 2/90. Find P(not a twin).

• P(twin) + P(not a twin) = 1 (Equation)

• 2/90 + P(not a twin) = 1 (Substitute)

• 2/90 – 2/90 + P(not a twin) = 1 – 2/90– (Subtract from both sides)• P(not a twin) = 88/90 = 44/45• Every 44 out of 45 people are not a twin.

Try These

• When you roll a dice, what is P(not 2)?

• 5/6

• What is the complement of an impossible event?

Finding the OddsFinding the Odds

• If PROBABILITY is a ratio of PART:WHOLE,

• Then an ODD is the ratio of PART: PART.Odds in Favor of an Event: – # of FAVORABLE outcomes– # of UNFAVORABLE outcomes.

Odds against an Event: – # of UNFAVORABLE outcomes– # of FAVORABLE outcomes.

Lets Try These

• What are the ODDS that a quarter shown at random from these has a least one human figure on it?

• What are the odds that a quarter chosen at random from the five shows a horse?

• What are the odds that it shows no horse?

And This One

• Consider the event of randomly choosing a quarter that shows the outline of a state.

• A) What are the odds in favor of the event?

• B) What are the odds against the event?