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 Total number of possible outcomes Probability, 0 < P < 1 Note that it cannot be greater than 1 or less than 0 P =

A Flip of a Coin What is the probability of getting a heads on any flip of the coin? Number of ways to obtained desired outcome Total number of possible outcomes 1 head 1 head or tails Since 1 head + 1 tail = 2 possible outcomes. P = ½ = 0.5 P = P =

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

How can calculate the probabilities from multiple coin tosses? The results in red above are for a perfect distribution of “penny” data. How do your results compare?

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?