Sec 9 6 Simulate Chance Events

all right so wrapping up here our module on probability now we're going to be talking little bit more about what it might look like to design simulation to model form of probability so example one says in board game there is two-ninth chance of drawing card that gives player double turn the remaining cards are single turns player wants to run simulation to estimate the probability of drawing two double turn cards in row assuming the first card is replaced and the deck is shuffled afterward so part says how can the player model this the chance of drawing two double turn cards in row and so then we're going to design simulation over this okay so on most of these designs we want something that's really easy to design right so spinner is nice easy design that we could do so that's where we're going to go with lot of these so i'm going to say they could design spinner now it says there's two-ninth chance of drawing card that gives player double turn so in other words that means two out of the nine cards must be double turn leaving seven out of the nine to not be double turn so i'm gonna design spinner and i'm gonna with nine sections and i'm going to do nine sections because figured out well if the probability is two ninths that means two out of nine must be double turn so that's why i'm going to go nine sections because two out of the nine so design spinner with nine sections and i'm going to label two of those sections label two sections with and i'm just because remember i'm just making this quick so i'm doing for double turn right don't necessarily need right double turn on the spinner because as i'm designing this simulation i'm going to know that stands for double turn so two labeled with for double turn and then the rest i'm going to label with an for single turn so there's gonna be seven left over so label two sections and seven sections for single turn okay so that's that's the spinner i'm going to design and then of course how am actually going to carry out this simulation well it says what's what's the probability you know of getting two double turn cards back to back right so that means i'd have to spin the spinner twice so each trial that is ran each trial will be two spins okay so would spend the spinner once see what it lands on spin the pin spinner again see what it lands on that'd be one trial and then continue doing that okay so i've designed the simulation now part says suppose the table shows the result of 10 trials of simulation represents the double turn the represents drawing single card which is kind of what said according to the results of the simulation what is the experimental probability so this is what actually happened right two-ninths was was the theoretical probability of player getting double turn right this is the experimental probability because we actually carried out the simulation of drawing two double turn cards in row so i'm looking for how many times did we get double d's right so it looked like it happened once there never again did get did we get those two d's so there was one time it happened out of how many trials looks like there was ten trials so one out of ten times it happened so as decimal that's one tenth as percent that's ten percent so then the experimental probability of drawing two double turn cards in row would be ten percent all right example two computer simulation with 50 trials is conducted to simulate drawing two cards from 52 card deck until two cards of the same value are drawn the graph shows the relative frequency of the number of times needed for the computer to draw two cards of the same value okay using the graph what's the experimental probability that less than four draws are needed to get the two cards of the same value now this does specify this time to write that probability as percent so the chart here gives us that relative frequency remember that relative frequency really that is that is our experimental probability now it said what's the experimental probability that it takes less than four draws to get those two cards of the same value so less than four i'm looking at one two and three draws so it looks like we had relative frequency of four hundredths we had relative frequency of one-tenth and then relative frequency of 28 hundredths for three add those all up i'm going to have my experimental probability which would be hundredths now since did specify to write this as percent then move my decimal two places to the right multiply it by hundred so that'd be forty two percent probability of it taking less than four drop four draws to get two cards of the same value