Probability – 1.6

Write each number as a percent Probability – Warm Up

1. = 3 ÷ 8 = = 0.375(100%) = 37.5% 2. 1 = = 11 ÷ 6 = 1.83 = 1.83(100%) = 183 % = (100%) = 0.43% 4. = 1 ÷ 400 = = (100%) = 0.25% = 1.04(100%) = 104% 6. 3 = 3(100%) = 300% Solutions Probability – Warm Up

There are two types of Probability: Experimental probability – P (event) = number of times the event occurs number of trials Theoretical Probability – P(A) = m n m = number of favorable outcomes n = number of equally likely outcomes

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 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 equally likely outcomes are in the sample space. 2 outcomes result in a multiple of =

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? Bb BBBBb bBbbb 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} The outcome bb is the only one for which a child will have blue eyes. So, P(blue eyes) = The theoretical probability that the child will have blue eyes is, or 25%.

Geometry Probability Geometric Probability = area that would give a favorable solution total area R = 1 Each ring has a width of 1 How do we find the probability of hitting the purple ring? Strategy?? In your own words, how would we get the probability of the purple ring

Probability For the dartboard above, 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) area of circle with radius 4r = 16 r 2 – 9 r 2 16 r 2 = 7 r 2 = (4r) 2 – (3r) 2 (4r 2 ) = 7 16 The theoretical probability of hitting the outer ring is, or about 44% Radius = 1 Each ring has a width of 1

Random Number Generator When actual trials are difficult to conduct, you can find experimental probabilities by using a simulation, which is the model of one or more events. To create a random number list on the graphing calculator, use the following keys: MATH RandInt ENTER Create a random number generator for the integers 1 to 10 Input: (1, 10)