Algebra A

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Algebra A

• 5-6 Probability and Odds
• Page 219

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QUICK QUIZ

• In your notebook, complete these
• Find 8 of 120.
• What percent is 12 of 48?
• 2 is 5 of what number?
• Find 10 of 240.
• Find 110 of 240.
• 750 is what percent of 250?

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5-6 Probability and Odds

• When you roll a single, six-sided die, numbered 1
  - 6, there are six possible numbers that can come
  up.
• Assuming the die is weighted fairly, all the
  numbers will come up on a regular basis.
• The chances that a particular number will come up
  is called the probability that the number will be
  rolled.

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5-6 Probability and Odds

• Probability
• WORDS The probability of an event is a ratio
  that compares the number of favorable outcomes to
  the number of possible outcomes.
• SYMBOLS
• NUMBERS P(rolling a 6)

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5-6 Probability and Odds

• The probability that an event will happen is
  between 0 and 1, inclusive.
• A probability of 0 means that the event is
  impossible.
• A probability of 1 means that an event is
  certain to happen.
• The closer a probability to 1, the more likely
  that it is to occur.

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5-6 Probability and Odds

• What is the probability that the sun will rise
  tomorrow morning?
• What is the probability the Redskins will win the
  Super Bowl this year?

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5-6 Probability and Odds

• What is the probability that the sun will rise in
  the West tomorrow?
• What is the probability that you will roll an
  even number with a 6-sided die?

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5-6 Probability and Odds

• When all possible outcomes have an equally likely
  chance of happening, the outcomes are said to be
  random.
• Is rolling a fair 6 sided die random?
• The odds that the tenth day of any month will be
  a weekday is that random?

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5-6 Probability and Odds

• Place 20 red ping-pong balls and 20 white
  ping-pong balls in a dark bag and mix them up.
  If you select a single pin-pong ball, is this
  selection random?
• You have made your one selection, and set that
  ping-pong ball aside. Now you choose another
  ping-pong ball. Is that event random?

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5-6 Probability and Odds

• Theoretical probability is what should occur or
  what is expected to occur.
• Experimental probability is what actually occurs
  during experiments.

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5-6 Probability and Odds

• If we flip a coin 10 times, what does the
  theoretical probability say will happen?
• Experiment.

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5-6 Probability and Odds

• ODDS
• WORDS The odds of an event occuring is a ratio
  that compares the number of favorable outcomes to
  the number of unfavorable outcomes.
• Symbols Odds

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5-6 Probability and Odds

• You have a bag with 6 red marbles, 3 blue marbles
  and 1 yellow marble. What are the odds of
  choosing a red marble?

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Practice
Playing Monopoly or Backgammon, you get to roll
again if you roll doubles. What is the
probability of rolling doubles?
Know
of ways a certain outcome can occur
Probability
of possible outcomes
Each die has 6 sides
Solve
Make a table showing all the combinations that
you could roll on a pair of dice as ordered pairs.
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Sample Space for Rolling two Die
Second die
Fi rs t d ie
1 2 3 4
5 6
1 2 3 4 5 6
(1,1) (1,2) (1,3) (1,4)
(1,5) (1,6)
(2,1) (2,2) (2,3) (2,4)
(2,5) (2,6)
(3,1) (3,2) (3,3) (3,4)
(3,5) (3,6)
(4,1) (4,2) (4,3) (4,4)
(4,5) (4,6)
(5,1) (5,2) (5,3) (5,4)
(5,5) (5,6)
(6,1) (6,2) (6,3) (6,4)
(6,5) (6,6)
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There are 6 ways to get doubles. There 36
possible outcomes.
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The probability of an event is always
between 0 and 1, inclusive. If an event cannot
happen, its probability is 0. If something is
certain to happen, its probability is 1
0
1
impossible
certain
50-50 chance
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0
1
impossible
certain
50-50 chance
100
50
0
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Probability
of ways a certain outcome can occur
Probability

of possible outcomes
Odds and Probability are expressed differently.

The probability of an event is always between
0 and 1 or 0-100.

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5-6 Probability and Odds

• More examples.