Probability
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Probability. What is probability?. In your own words… Probability of an event is the number from 0 to 1 that indicates the likelihood the event will occur. An event is an outcome or collection of outcomes Probabilities can be written as a decimal, a percent, or a fraction.

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What is probability
What is probability?

  • In your own words…

  • Probability of an event is the number from 0 to 1 that indicates the likelihood the event will occur.

  • An event is an outcome or collection of outcomes

  • Probabilities can be written as a decimal, a percent, or a fraction.


What is probability1
What is probability?

  • For example, when rolling a dice there are six possible outcomes or events: 1, 2, 3, 4, 5, or 6.

  • A different event could be “rolling an odd number”. So, the event would be 1, 3, or 5


Probability1
Probability

  • Using a number line can help describe the probability of an event.

Event is more likely not to occur

Event is more likely to occur

P = 1

Event is certain

to occur

P = 0

Event will not occur

P = .5

Even is equally

likely to occur

or not occur


Theoretical probability
Theoretical Probability

  • When all outcomes are equally likely, the theoretical probability that an event A will occur is:

  • P(A) = number of outcomes in event A ÷ Total number of outcomes

  • The theoretical probability of an even tis often simply called the probability of the event.


Find probabilities of an event
Find Probabilities of an Event

  • You roll a standard six-sided die. Find to probability of:

    • Rolling a 5

    • Rolling an even number


Find probabilities of an event1
Find Probabilities of an Event

  • There are 6 possible outcomes. Only 1 outcome corresponds to rolling a 5.

    P(rolling a 5) = =

# of ways to roll a 5

# of ways to roll the die


Find probabilities of an event2
Find Probabilities of an Event

  • Find the probability of rolling an even number.

  • A total of 3 outcomes correspond to rolling an even number: a 2, 4, or 6

    P(rolling even number) =

    =

# of ways to roll an even number

# of ways to roll the die


Find probabilities of an event3
Find Probabilities of an Event

  • You have an equally likely chance of choosing any integer from 1 through 20. Find the probability of the given event.

  • A perfect square is chosen.

  • A factor of 30 is chosen.


Answers
Answers

  • A perfect square is chosen

  • A factor of 30 is chosen


Use permutations or combinations
Use Permutations or Combinations

  • A community center hosts a talent contest for local musicians. On a given evening, 7 musicians are scheduled to perform. The order in which the musicians perform is randomly selected during the show.


Use permutations or combinations1
Use Permutations or Combinations

  • What is the probability that the musicians perform in alphabetical order by their last names? (Assume that no two musicians have the same last name)


Use permutations or combinations2
Use Permutations or Combinations

  • There are 7! different permutations of the 7 musicians. Of these, only 1 is in the alphabetical order by last name.

  • So the probability of is:

    P(alphabetical order) =


Use permutation or combinations
Use Permutation or Combinations

  • You are friends with 4 of the musicians. What is the probability that the first 2 performers are your friends?


Use permutations and combinations
Use Permutations and Combinations

  • There are 7C2 different combinations of 2 musicians. Of these, 4C2 are 2 of your friends.

  • So, the probability is:

    P(first 2 performers are your friends) =


Odds

  • You can also use odds to measure the likelihood that an event will occur.

  • Odds measure the chances in favor of an event occurring or the chances against an event occurring.


Odds

  • When all outcomes are equally likely, the odds in favor and not in favor of an event A are as follows:

    Odds in favor of event A =

    Odds not in favor of event A =

  • You can write the odds in favor of or against an event in the form or in the form a:b.

# of outcomes in A

# of outcomes not in A

# of outcomes not in A

# of outcomes in A


Find odds
Find odds

  • A card is drawn from a standard deck of 52 cards. Find:

    • The odds in favor of drawing a 10

    • The odds against drawing a club


Find odds1
Find odds

  • Odds in favor of drawing a 10 =

    = or 1:12

  • Odds against drawing a club =

    = or 3:1

# of non-clubs

# of tens

# of non-tens

# of clubs


Find odds2
Find Odds

  • What are the odds:

    • In favor of drawing a heart

    • Against drawing a queen


Experimental probability
Experimental Probability

  • Sometimes it is not possible or convenient to find the theoretical probability of an event.

  • In such cases, you may be able to calculate an experimental probability by performing an experiment, conducting a survey, or looking at the history of the event.


Experimental probability1
Experimental Probability

  • When an experiment is performed that consists of a certain number of trials, the experimental probability of an event A is given by:

    P(A) =

# of trials where A occurs

Total # of trials


Geometric probability
Geometric Probability

  • Some probabilities are found by calculating a ratio of two lengths, areas, or volumes.

  • These are called geometric probabilities


Geometric probability1
Geometric Probability

  • Length

  • Area

  • Volume

area of smaller object

volume of smaller space

length of smaller segment

total length

total area

total volume


Geometric probability2
Geometric Probability

  • Darts and Bulls-eye


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