Transcript Probability 9/14

Probability
Predictions
Ch. 1, Act. 5
Probability
• The study of random events.
• Random events are things that happen without
predictability – e.g. the flip of a coin.
• Random events in large numbers are more
predictable
Determining Probability
• Probability (P) of an event is defined as the
ratio of the number of ways a desired
outcome may occur divided by the total
number of possible outcomes:
Number of ways to obtained desired outcome
P=
Total number of possible outcomes
• Probability, 0 < P < 1
• Note that it cannot be greater than 1 or less than
0
A Flip of a Coin
• What is the probability of getting a heads on
any flip of the coin?
P = Number of ways to obtained desired outcome
Total number of possible outcomes
P=
1 head
1 head or tails
Since 1 head + 1 tail = 2 possible outcomes.
P = ½ = 0.5
Roll of the Dice
• What is the probability of rolling a 5?
• Since there are 6 sides to a die, and there is only
one side with a 5, the probability is:
P = 1/6
• What is the probability of rolling a 2 or a 5?
• Since there are 6 sides to a die, and there are is
a side each with a 2 and a 5, the probability is:
P = 2/6, or 1/3 (0.33)
A Deck of Cards
• What is the probability of pulling an ace from a
deck of cards?
• Since there are 4 aces in a deck of 52 cards:
P = 4/52 = 1/13
• What is the probability of pulling an ace of spades
from a deck of cards?
• Since there is only one ace of spades in a deck of 52
cards:
P = 1/52
Predictability of Random Events
• While the flip of a coin, roll of a dice or a
hand of poker cannot be determined from
one flip, roll or hand to the next, many coin
tosses, roll of the dice or hands in poker can
be determined with a relatively accurate
level of predictability.
• What does this mean?
• As you increase the number of experimental trials,
the outcome of an event becomes more predictable,
and aligned with the theoretical prediction.
How can we predict multiple coin tosses?
Pascal’s Triangle
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Activities 3 & 4 Revisited
• In Activity 3, you discovered a pattern.
• If you took only one measurement, could you have
concluded that the circumference to diameter ratio was
a constant?
• With our “paper toss”, would you have been as
convinced of the outcome with only one run?