1-6 Probability M11.E.3.1.1: Find probabilities for independent, dependent, or compound events and represent as a fraction, decimal, or percent

Objectives Experimental Probability Theoretical Probability

Vocabulary Experimental Probability of event = P(event) Number of times the event occurs Number of trials =

Finding Experimental Probability A player hit the bull’s eye on a circular dartboard 8 times out of 50. Find the experimental probability that the player hits the bull’s eye. P(bull’s eye) = = 0.16, or 16% 8 50

Probability Describe a simulation you could use that involves flipping a coin to find the experimental probability of guessing exactly 2 answers out of 6 correctly on a true-false quiz. Getting heads with a flip of a coin has the same probability as guessing the correct answer to a question on a true-false test. So, let heads represent a correct answer and tails represent an incorrect answer. To simulate guessing the answers for a six-question true-false test, flip a coin six times. Record the number of heads. Repeat 100 times. Count to see how many times heads came up exactly twice. Divide this number by 100. The result is the experimental probability that the simulation gives for guessing 2 correct answers out of 6.

Vocabulary If a sample space has n equally likely outcomes and an event A occurs in m of these outcomes then the theoretical probability of event A is P(A) =

Probability Find the theoretical probability of rolling a multiple of 3 with a number cube. To roll a multiple of 3 with a number cube, you must roll 3 or 6. 2 6 6 equally likely outcomes are in the sample space. 2 outcomes result in a multiple of 3. 1 3 =

Probability Brown is a dominant eye color for human beings. If a father and mother each carry a gene for brown eyes and a gene for blue eyes, what is the probability of their having a child with blue eyes? B b B BB Bb b Bb bb Gene from Father Gene from Mother Let B represent the dominant gene for brown eyes. Let b represent the recessive gene for blue eyes. The sample space contains four equally likely outcomes {BB, Bb, Bb, bb}. 1 4 The outcome bb is the only one for which a child will have blue eyes. So, P(blue eyes) = . 1 4 The theoretical probability that the child will have blue eyes is , or 25%.

Probability For the dartboard in Example 5, find the probability that a dart that lands at random on the dartboard hits the outer ring. P(outer ring) = area of outer ring area of circle with radius 4r = (area of circle with radius 4r) – (area of circle with radius 3r) = (4r)2 – (3r)2 (4r2) = 16 r 2 – 9 r 2 16 r 2 = 16 r 2 7 r 2 = 7 16 The theoretical probability of hitting the outer ring is , or about 44%. 7 16