Probability

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Probability

• What will Be?

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• The probability P, of an event is the RATIO of
  successful outcomes, called Successes, to all
  outcomes of the event, called Possibilities.

P(E)
BACK
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• Probability of an event is a Number between 0
  and 1.

BACK
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Certain and impossible
An event(E) that is certain to happen, then
P(E) 1
e.g. A die is thrown
P(integers)
1
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Certain and impossible
An event(E) that is impossible to happen, then
P(E) 0
P(E) 0
P(E) 0
e.g. A die is thrown
P(getting a 0)
0
BACK
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CHANCE

• Chance is how likely it is that something will
  happen. To state a chance, we use a percent.

½ Probability
0
1
Equally likely to happen or not to happen
Certain to happen
Certain not to happen
Chance
50
0
100
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Likelihood
When the probability is greater than 0.5, implies
the event is likely to happen
When the probability is smaller than 0.5, implies
the event is unlikely to happen
BACK
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Applied Probability
What is the probability that the sun will rise in
the west tomorrow?
Zero
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Probability of getting a head when flipping a
coin.
0
1
BACK
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The possible outcomes
Example 1
An unbiased coin
The total possible outcomes is head (H) or Tail
(T)
P(H)
and
P(T)
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Applied Probability
If you tossed a quarter 50 times, how many times
should it land on tails?
25 times
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Probability of getting a head when flipping a
coin.
0
1
0.5
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What is the Probability of Rolling a 5 or 6?
Total possible outcomes is 6.
P( )
5 or 6
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Special Dice
What is the possible outcome of the above case?
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You Try
Probability

• A jar contains 12 blue ,8 green, and 5 red
  marbles
• If you reach in choose 1
• What is the P it is blue?
• What is the P it is not blue?
• What is the P it is not black?

BACK
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Probability (Your Turn)

• What is the P it is blue?
• P 12/25 .48
• What is the P it is not blue
• P 13/25 .52
• What is the P it is not black
• P 25/25 1

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Example
There are 5 red marbles, 3 green marble and 2
black marbles
5
P( )
red marbles
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Two Independent Events
Two events are said to be mutually exclusive
events if both events cannot happen at the same
time.
You Try
Example
A die is rolled
Event A getting a
Event A getting a
Event B getting a
Event B getting a
What is the probability of first rolling a 3,
then rolling a 6?
BACK
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Example
If a card is drawn at random from a pack of 52
playing cards, find the probability that
Either a king or a queen is drawn
P(king or queen)
P(king) P(queen)
king
queen
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Example of Multiplication of Probabilities
Two cards are drawn one after the other at
random from a pack of 52 play cards. The first
card drawn is put back into the pack and the
pack is shuffled before the second card is drawn.
Find the probability that both cards drawn are
the king of clubs.
You Try
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(a) P(first king)
P(second club)
P(first king and second club) P(first king) X
P(second club)
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(b) P(first king of clubs) P(second king of
clubs)
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• An algebra Class has 17 boys and 16 girls. One
  student is chosen at random. The Probability
  that the student is a girl is

Number of girls
P
Number of students
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• of students 16 17
• of students 33
• of girls 16
• P 16/33 .485

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Definition of Odds

• The odds of an event is the ratio of success to
  failures.

BACK
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Whats the probability of

• getting a 6 on a dice
• a letter chosen from the word RABBIT is a B
• getting a number less than 3 on a dice
• a pupil picked at random from the class is in
  your tutor group
• a persons birthday is on a Sunday this year

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Rolling a fair 6 sided die

• On a probability scale mark the probability of
  rolling
• a 5
• an odd number
• a prime number
• zero
• a number between 0 and 7
• a number greater than 2

D A BC F E
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Probability
Probability is the measure of the likelihood of
an event. Some events are certain, some
possible, some impossible.
An impossible event occurring has a probability
of 0.
An event that has a chance of occurring but not
certain has a probability greater than 0 and less
than 1.
An event that is certain to occur has a
probability of 1.
The probability of an event will always be 0 lt e
lt 1
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Probability

• What will Be?