Transcript File
Lesson 14 Determining the theoretical probability of an event Probability terms •Sample space is the set of all possible outcomes of an event- tossing a fair coin has 2 equally likely outcomes, so has a sample space of 2 •Simple event is an event having only one outcome- rolling a 5 on a dice •Theoretical probability of an outcome is found by finding the ratio of favorable outcomes to all possible outcomes • favorable outcomes • all possible outcomes Identifying sample spaces • A number cube labeled 1-6 is rolled. • List the outcomes for each event: • 1. a number less then or equal to 3 • 2. an odd number • 3. an even number • 4. a multiple of 3 • 5. a prime number Complement of an event • The set of all outcomes that are not in a given event. • If heads is the desired outcome when tossing a coin, then tails is the complement • The sum of an event and its complement = 1 • P (event) + P (not event) = 1 hint !!! •Probability can be expressed as fractions, decimals, or percents Calculating theoretical probability • Suppose there are 4 green, 3 blue and 3 red marbles in a bag. Give each answer as a decimal and percent, • 1. what is the probability of choosing a red marble? P (red)= 3/10,, .3, 30% • 2. what is the probability of choosing a marble that is not red? • P (not red)= 7/10, .7 , 70% OR • P (not read) = 1-P(red)= 1-.3= .7 Chance • Chance is the likelihood of an event occurring. • Calculating chance• Ex: in a bucket there are 10 balls numbered as follows: 1,1,2,3,4,4,4,5,6,6. • A single ball is randomly drawn from the bucket. • What is the probability of drawing a ball with a number greater than 4? • Is there a greater chance of drawing a number greater than 4 or a 1? solution •P (greater than 4) = 3/10 or .3 •P (1) = 2/10 = .2 •.3 > .2 so there is a greater chance of drawing a number greater than 4 Lab 1 generating random numbers • A set of random integers has no pattern. We can generate random numbers by rolling a dice or drawing numbers out of a hat. We can also generate random integers by using a graphing calculator. Generate 3 random numbers between 1 and 12 • 1. Press MATH and then the right arrow key 3 times until you get to PRB • 2. Go down to 5:randInt( • 3. press enter • 4. identify the range of values you want1 through 12 by pressing 1,12) • 5. press enter to get the 1st integer • 6. press enter 2 more times to get 2 more random integers. Lab practice • Jared lost the dice to his favorite board game, but he does have a graphing calculator. According to the rules, the player should throw 2 dice and move the total number of spaces shown on the top of the 2 dice. • 1. What range of numbers does a single dice generate? What should he enter in his calculator to simulate the dice? • 2. How can he simulate rolling 2 dice? • 3.simulate Jared taking 3 turns. What number of spaces will he move in each turn? What is the total number of spaces moved? Investigation 1 determining the probability of an event • Probability is the measure of how likely a given event will occur. • An outcome is a possible result of a probability experiment. • An event is an outcome or set of outcomes in a probability experiment Range of probability • Impossible • unlikely as likely as not certain likely • ______________________________________________________ • 0% 50% 100% Describe each event below as impossible, unlikely, as likely as not, likely, or certain. • 1. Jake rolls a number less then 7 on a dice. • Certain • 2. February will have 30 days • Impossible • 3. A tossed coin will land on heads • As likely as not • 4. Shayla will correctly guess a number between 1 and 100 • unlikely Experimental probability • Experimental probability is the measure of how likely a given event will occur based on repeated trials. • Experimental probability= number of times an event occurs • number of trials Activity • follow directions to complete investigation 1 activity Experimental probability in sports • A player's batting average is the probability of a player getting a hit based on his previous at bats. It is usually expressed as a decimal to the thousandths place. • If a player gets 8 hits in 25 at bats, what is the probability that he will get a hit on his next at bat? • 8/25= .320 Random events • A random event is an event whose outcome cannot be predicted. • Ex. Drawing a card labeled 8 from a bin of cards, each labeled with a number from 1 to 100, is a random event. • We could conduct an experiment and find the experimental probability, but sometimes it is not practical to do this. • So sometimes we perform a simulation of a random event using models such as dice, spinners, coins, or random number generators. activity • Saxon O's cereal is having a contest. Each box of cereal contains a prize piece and claims that 1 in 8 pieces is a winner. Conduct a simulation to determine the experimental probability of winning a prize piece within 50 boxes of cereal. • 1. use the digits 1 through 8 • 2. generate 50 random numbers • 3. what is the probability of winning a prize, according to your simulation. • 4. how does your answer compare to the company's claim?