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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?