Probability

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Probability
Probability is one way to measure the chance that
an event will occur.
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The study of probability allows mathematicians
and scientists to make predictions when the
outcomes of events are not certain.
Probability is essential to the study and
prediction of weather patterns, developing
medicines, hereditary traits, and most
experiments in science.
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Lets ReviewBasic Probability
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Types of Probability

• Theoretical Probability
• Based on knowing all of the equally likely
  outcomes.
• We use the formula

Experimental Probability Based on repeated trials
of an experiment. We use the formula
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To find the theoretical probability (p) of an
event, we use

• For example
• What is the probability of rolling a six on a die?

Number of favorable outcomes.
Number of possible outcomes.
Probability of rolling a 6
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A spinner has 4 equal sectors colored yellow,
blue, green and red.
What are the chances of landing on blue after
spinning the spinner?
What are the chances of landing on red?
What is the probability of landing on purple
after spinning the spinner?
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Whats New?
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Compound Events

• Involve two or more simple events. Compound
  events involve the use of the words and and or.

Disjoint
Independent
Dependent
and
or
Events do not affect each other.
Events affect each other.
Events can not happen at the same time.
P(a) and P(b) P(a b)
P(a) or P(b) P(a b)
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Independent Events

• Two events are independent when the outcome of
  one event has no effect on the outcome of another
  event.

Event 1 tossing a coin and it landing on heads.
Event 2 tossing a number cube and getting an odd
number.
When finding the probability of two independent
events, multiply the probabilities of the two
events to get the total probability.
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Practice

• Greg has 5 red tiles, 3 green tiles, and 2 blue
  tiles in a paper bag. If he chooses a tile at
  random, returns it to the bag, and then chooses a
  second tile, what is the probability that the two
  tiles will be green and blue in that order?

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Practice

• The weather forecast reports that the probability
  of rain today is 30 and the probability of rain
  tomorrow is 50. What is the probability that it
  will rain on both days?

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Practice

• What is the probability of tossing a penny and
  landing on tails, rolling a number cube with
  faces numbered 1 through 6 and landing on an odd
  number, and this spinner landing on x?

W X Y Z
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Dependent Events

• Two events are dependent when the outcomes of
  one event are effected by the outcomes of the
  other.

Anna has a bag that contains ten gumballs 4 red,
5 yellow and 1blue.
What is the probability of pulling out a red
gumball followed by a blue gumball in that order
when you draw two gumballs from the bag without
returning the first gumball to the bag?
What is the probability of pulling out a red
gumball followed by a blue gumball in that order
when you draw two gumballs from the bag without
returning the first gumball to the bag?
Find the probability of the first event and
multiply it by the probability of the second
event (dont forget you did not replace the
marble).
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Practice

• A bag contains 3 yellow, 3 green, and 3 blue
  marbles. What is the probability of drawing a
  blue marble followed by a yellow marble in that
  order when you draw two marbles from the bag
  without returning the first marble to the bag?

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Practice

• Taylor has a jar filled with 21 green olives and
  15 black olives in it. If she takes two olives
  out of the jar without replacement, what is the
  probability that the first olive will be black
  and the second olive will be green?

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Practice

• Bo asked Luke to guess what month and day of the
  week he was born. If all things are considered
  equal, what was the probability that Luke guessed
  the month and the day of the week correctly?

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Disjoint Events

• Two or more events are disjoint when the
  outcomes of the events can not happen at the same
  time.
• AKA Mutually exclusive

Donna has a number cube numbered 1 through 6. If
she rolls the cube once, what is the probability
that she will roll either a 3 or 4?


or
P(3)
P(4)
Find the probability of the first event and add
it to the probability of the second event.
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Practice

• If you flip a coin twice, what is the probability
  that a head or tail will land up on the first
  flip?

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Practice

• Spinning red or green on a spinner that has four
  equal sectors colored red, green, blue, and yellow

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Practice

• What is the probability of drawing a black marble
  or a red marble from a bag that contains 4 white
  marbles, 3 black marbles, and 2 red marbles?

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Practice

• What is the probability of choosing either a boy
  or a girl from a class of 13 boys and 17 girls?