Theoretical Probability – Math 6

Vocabulary Probability – a number that measures the likelihood that an event will occur Likelihood – the change or the odds Favorable outcomes- the outcomes of an event Possible outcomes – the possible results Independent event - two events whose occurrence of one event DOES NOT affect the likelihood that the other event will occur (coin, spinner, dice, with replacement) Dependent event - two events whose occurrence of one event DOES affect the likelihood that the other event will occur (without replacement)

Example Tell whether the events are independent or dependent. Explain. You flip heads on one coin and tails on another coin. Your teacher chooses one student to lead a group, and then chooses another student to lead another group. You choose a marble from a bag and set it aside. Then you choose another marble from the bag. You choose a marble from a bag, record its color, and place it back into the bag. Then you choose another marble from the bag.

Things to Know Note: Probabilities can be written as fractions, decimals, or percents.

Examples the sun rising tomorrow = 1 math homework = 0.75 winning the softball game = 0.50 skipping breakfast = 0.25 a winter in Vermont with no snow = 0 Equally likely: number cube Not equally likely: spinner with sections that are not all the same size

Things to Know

Example You roll the number cube. What is the probability of rolling an odd number? In example 2, what is the probability of rolling a number greater than 4?

Finding the Probability of Two Independent Events Step 1: Find the probability of A = P(A) Step 2: Find the probability of B = P(B) Step 3: Multiply the probability of A by the probability of B = P(A) x P(B) Step 4: Simplify your fraction

Examples P(tails and even) To win the grand prize, Ted has to choose one of 10 keys to match with one of 3 treasure chests. What are Ted’s chances of winning? Sarah placed 4 yellow chips and 8 pink chips into a bag. She selected 1 chip without looking, replaced it, and then selected a second chip. Find the probability that she first selected a yellow chip and then selected a pink chip.

Finding the Probability of Two Dependent Events Step 1: Find the probability of A = P(A) Step 2: Find the probability of B after A has occurred = P(B after A) Step 3: Multiply the probability of A by the probability of B after A has occurred = P(A) x P(B after A) Step 4: Simplify your fraction

Example You have four $20 bills and three $10 bills. You randomly choose a bill from your wallet to pay for lunch. You need more money, so you choose another bill. What is the probability that you choose a $20 bill, then a $10 bill? You are guessing at two questions on a multiple choice test. Each question has three choices: A, B, and C. Suppose you can eliminate one of the choices for each question. How does this change the probability that your guesses are correct?

Assignment