Chapter 12: Probability & Statistics. Notes #2: Simple Probability and Independent & Dependent Events and Compound Events
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1 Chapter 12: Probability & Statistics Notes #2: Simple Probability and Independent & Dependent Events and Compound Events Theoretical & Experimental Probability 1 2 Probability: How likely an event is to occur Equally Likely Outcomes: Have the same chance of occurring Outcome: Each possible result of an experiment Sample Space: The set of possible outcomes Event: An outcome or set of outcomes 3 Favorable outcomes: The outcomes in a specified event (the outcomes you re looking for) Theoretical Probability: P(event)=number of favorable outcomes number of outcomes in sample space 4 Ex 1: A CD has 5 upbeat dance songs and 7 slow ballads. What is the probability that a randomly selected song is an upbeat dance song? Ex 2: A red number cube and a blue number cube are rolled. If all numbers are equally likely, what is the probability that the sum is 7? 5 6 1
2 Complement: The set of all outcomes that are not in E (the event). P(not E)=1-P(E) Ex 3: The game Battleship is played with 5 ships on a 100-hole grid. Players try to guess the locations of their opponent s ships and sink them. At the start of the game, what is the probability that the first shot misses all targets. Ship number Number of holes #1 2 #2 3 #3 3 #4 4 # Ex 4: Each student received a 4-digit code to use the library computers, with no digits repeated. Hannah received the code What was the probability that she would receive a code of consecutive numbers. Geometric Probability: Determined by a ratio of lengths, areas, or volumes Ex 5: Three semicircles with diameters 2, 4, and 6 are arranged as shown in the figure. If a point inside the figure is chosen at random, what is the probability that the point is inside the shaded region? 9 10 Experimental Probability: Estimated probability based on an experiment Ex. prob. = number of times the event occurs number of trials Ex 6: The bar graph shows the results of 100 tosses of an oddly shaped number cube. Find the experimental probability of a) rolling a 3 b) rolling a perfect square c) Rolling a number other than
3 Independent Events If one occurrence does not affect the probability of another Independent & Dependent Events Probability of Independent Events P(A and B)=P(A)P(B) Ex 1: Find the probability of spinning a green and then a green again on the spinner. Ex 2: Find the probability of spinning red, then green, and then red on the spinner. Dependent Events The occurrence of one event affects the probability of the other. Conditional Probability The probability of an event given that event A has occurred. P(B A) Probability of Dependent Events P(A and B)=P(A)P(B A) Ex 3: Two number cubes are rolled- one red and one blue. Explain why the events are dependent. Then find the indicated probability. a)the red cube shows a 1, and the sum is less than 4. Ex 4: The table shows the approximate distribution of votes in Texas five largest counties in the 2004 presidential election. Find the probability that a)a voter from Tarrant County voted for Bush b)the blue cube shows a multiple of 3 and the sum is 8. b)a voter voted for John Kerry and was from Dallas County
4 Ex 5: Two cards are drawn from a deck of 52. Determine whether the events are independent or dependent. Find the probability of a)selecting two aces when the first card is replaced. b)selecting a face card and then a 7 when the first card is not replaced. Compound Events Compound Event: An event made up of two or more simple events. Mutually Exclusive Events: Events that cannot both occur in the same trial. P(AUB)=P(A)+P(B) Ex 1: A drink company applies one label to each bottle cap: free drink, free meal, or try again. A bottle cap has a 1/10 probability of having free drink and a 1/25 probability of having free meal. a)explain why they are mutually exclusive b)what is the probability that a cap is labeled free drink or free meal Ex 4: Of 3510 drivers surveyed, 1950 were male and 103 were color-blind. Only 6 of the color-blind drivers were female. What is the probability that a driver was male or was colorblind?
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