Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Find the probability of an event by using theoretical, experimental, and simulation methods. Vocabulary An outcome is the result of a single trial Sample space is all possible outcomes An event is any outcome or group of outcomes. The outcomes that match a given event are called favorable outcomes. EX: Probability Tells how likely it is that an event will occur. Abbreviated P(event) “the probability of an event” Ex: P(even) That is, the probability of rolling an even number Probability ranges from 0 to 1 Theoretical When all possible outcomes are equally likely, you can find the theoretical probability. Uses math reasoning 3 6 EX: P(even) = = 1 2 Can be written as a fraction, decimal, or percent. Practice 2 8 P(distance less than Earth’s) = = 1 4 Complement of an Event All outcomes in the sample space that are NOT in the event. The sum of the probabilities of an event and its complement is 1. P(event) + P(not event) = 1 So, to find the probability of the complement of an event: P(not event) = 1 – P(event) Practice Find P(Drink A) P(Drink A) = 2 5 So P(not drink A) = 1 – P(Drink A) 2 5 P(not drink A) = 1 - = 3 5 Experimental Based on data collected from repeated trials. Ex: out of 1000 skateboards inspected, 992 were found to have no defects. P(no defects) = 992 1000 = .992 𝑜𝑟 99.2% Using Experimental Probability Out of 500 households, 197 have dogs. If your town has 24800 households, how many are likely to have dogs? P(own dog) = 197 500 = 0.394 Multiply 0.394 ∙ 24800 9771.2 Estimate: about 9770 households will own dogs. Simulation If an experiment is unreasonable or difficult to conduct, you can estimate the experimental probability by using a simulation. Ex: on a multiple choice test, each item has 4 choices. What is the probability that you will pass the test by guessing at least 6 out of 10 correctly? Use a calculator to create the simulation. Let the numbers 1, 2, 3, 4 represent your 4 options and let the number 1 represent a correct choice. Use MATH, move right to the PRB menu and choose randInt( Type randInt(1,4,10) to represent choosing digits 1-4 a total of 10 times. Continued You can scroll left and right to view the whole outcome. Write down the number of 1’s your calculator generated from your first trial. This is the number of questions you guessed correctly. Do this 19 more times so that we have 20 trials (taking the test 20 times). The goal was to guess at least 6 correct. Count number of times this occurred. Write the experimental probability out of your 20 trials. Using Combinatorics What is the theoretical probability of being dealt exactly two 7’s in a 5-card hand from a standard 52 card deck? We need to know the number of combinations of two 7’s 4C2 since there are four 7’s and we want 2 The number of combinations of 3 non-7’s 48C3 since there are 48 non-7’s and we want 3 The number of 5 card hands with two 7’s and three non-7’s is the product 4C2· 48C3 The sample space is all 5 card hands 52C5 So the probability is 4C2· 48C3 52C5 About 4% Assignment Odds p.685 #9-23