Understanding Probability

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• UnderstandingProbability

What are the Chances???
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Probability
Outcomes

• _______________ are the possible results of
• an action. There are ____ outcomes for
• rolling a single cube. They are
• An __________ is any outcome or group of
• outcomes. For example, rolling a number
• larger than 4 is an that corresponds
  to
• two different outcomes (5 and 6).

6
1, 2, 3, 4, 5, 6.
event
event
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Probability
Probability

• The _______________ of something happening
• is the chance of it occurring.
• It is often written as a ratio comparing the
• favorable outcomes with the number of
• possible outcomes.Probability of an event
• P(event)
• The probability will always be between 0 (not
  possible)
• and 1 (must happen)

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Fun with Probability

• In 1998, The odds of winning the California Super
• Lotto Jackpot are 1 in 18 million. (The odds now
  are
• over 1 in 41 million-they changed the format)
• Based on 1998 odds
• If one person purchases 50 Lotto tickets each
  week, they will win the jackpot about once every
  5,000 years.
• If a car gets 25 miles per gallon, and a gallon
  of gas is bought for every Lotto ticket bought,
  there will be enough gas for about 750 round
  trips to the moon before the jackpot is won.
• It is three times more likely for a person
  driving ten miles to buy a Lotto ticket to be
  killed in a car accident than to win the jackpot.

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Fun with Probability

• You have better chance for the following events
  to happen long before you ever win the lottery
• Dealt a royal flush on the opening hand in a
  poker game (1 in 649,739).
• Killed by terrorists while traveling abroad (1 in
  650,000).
• Die from flesh-eating bacteria (1 in 1 million).
• Get heart disease caused by eating a steak a week
  (1 in 48,000).
• Killed by a lightning strike (1 in 30,000).

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Two Kinds of Probability

• Theoretical probability describes the number
• of outcomes that occur.
• Experimental probability describes the
• number of outcomes that occur.

should
do
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Probability

• All probabilities range from 0 to 1.

Probability
Probability
less likely
more likely
0 Impossible event
1 Certain event
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Probability
complement
The ______________ of an event is the opposite of
that event. The events no rain and rain are
of each other.
complement
Probability
The probability of an event plus the probability
of its complement always equals 1.
P(event) P(not the event) 1
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Example 1
You have different coins in your pocket a
penny, a nickel, a dime, a quarter, and a
half-dollar. You pull out one coin at random.
What is the probability that the coin you take
out is worth less than ten cents?
Probability
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Example 1
How many coins are less than ten
cents?(favorable outcomes)
2
How many coins are there to choose
from?(possible outcomes)
5
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Example 1
You have different coins in your pocket a
penny, a nickel, a dime, a quarter, and a
half-dollar. You pull out one coin at random.
What is the probability that the coin you take
out is worth less than ten cents?
Probability
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Example 2
Probability
P(twin) P(not a twin) 1
Write an equation
Substitute.
Simplify.
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Finding Odds
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Example 3
The reverse sides of five quarters are shown
below. What are the odds that a quarter chosen
at random from these has at least one human
figure on its tail side?
3 have a human figure
2 do not.
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Check Understanding
INDIANA
Suppose you select a letter at random from the
word INDIANA.
What is the probability of selecting the letter
?
What is the probability of not selecting the
letter A ?
What is the probability of selecting the letter C
?
What are the odds in favor of selecting a vowel?
A
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Check Understanding - Answers
Suppose you select a letter at random from the
word INDIANA.
What is the probability of selecting the letter A
?
What is the probability of not selecting the
letter A ?
What is the probability of selecting the letter C
?
0
What are the odds in favor of selecting a vowel?
A