 Percentages

 Write the percent as a decimal. 54%

 Write the decimal as a percent

 Write the fraction as a percent. 3/8

 GOAL: Determine theoretical and experimental probability.

 What are some characteristics of dice?

 Sample space is the set of all possible outcomes  example: When rolling a 6-sided die, the possible outcomes are: {1,2,3,4,5,6}

 Theoretical Probability can be used when a sample space has equally likely outcomes, and we know it for a fact  example: Each side is ___________ likely when rolling a six- sided die.

Theoretical Probability with Coins  Find the probability of a coin landing on tails.

Theoretical Probability with Cards  Find the probability of choosing a queen when randomly selecting a playing card from a standard deck.

Biology Connection  In genes, there are dominant (G) and recessive (g) traits. Each person carries 2 traits. If at least one trait is dominant (GG or Gg), then the person portrays that trait. Only if both are recessive (gg) does the person portray the recessive trait. When a parent has both a dominant and a recessive gene, then the two genes are equally likely to be passed to a child.  Immunity to poison ivy is a dominant trait. Suppose that a child has two parents who both have just one dominant poison ivy immunity gene. What is the theoretical probability that the child will be immune?

 Choose one of the following:

Value# of occurences  Conditions:

Value# of occurences

Experimental Probability with Sports  When the University of Texas won college football’s national championship in the 2006 Rose Bowl game, its quarterback completed 30 of 40 passes. Find the experimental probability of the quarterback completing a pass.

Experimental Probability with Fish  A pond contains three types of fish: bluegills, red gills, and crappies. Each fish in the pond is equally likely to be caught. You catch 120 fish and record the type. Each time, you release the fish back into the pond. The frequency distribution shows your results. If you catch another fish, what is the probability that it will be a bluegill? Fish TypeNumber of times caught, f Bluegill39 Red gill51 Crappy30 Total = 120

 If actual trials are difficult to conduct, you can find experimental probabilities by using a simulation, or a model of one or more events.

Experimental Probability with a Simulation  Suppose you take a true-or-false quiz and guess for answers at random. What is an experimental probability that you will get at least three answers correct?  15 trials  Digits: o 0-4 correct o 5-9 incorrect

Geometric Probability  Suppose that all the points on the circular dartboard shown below are equally likely to be hit by a dart you have thrown. Find the probability of scoring at least ten points, given that the dart lands somewhere within the area of the dartboard.  Is this theoretical or experimental?

Venn Diagram Probability  In a class of 147 students, 95 are taking math, 73 are taking science, and 52 are taking both math and science. One student is picked at random. Find each probability.  P(taking science)  P(not taking math)  P(taking neither math nor science)  Is this theoretical or experimental? M S

 In a town of 50 people, 40 own cats, 18 own dogs, and 12 own cats and dogs. If one person is randomly selected, what is the probability that he/she owns a cat and not a dog?  Create a Venn diagram to assist.  What is the difference between theoretical and experimental probability?