Understanding Probability in Events
Explore concepts of probability in various events like rolling a die, compound events, simple events, and spinner probability. Learn how to calculate probabilities of different outcomes and understand the difference between single and compound events. Discover key principles in probability theory and apply them to real-life scenarios like playing games and making decisions.
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What is the probability of the following: 1. Rolling a 4 on a die 2. Rolling an even number on a die 3. Rolling a number greater than 2 on a die Answer the following: 4. 5. *BellWork
*How to Hit it Big in the Lottery! Probability of Compound Events
*Directions 1. Students play in pairs and take turns. 2. After rolling the number cubes, Player 1 records the sum of the numbers. 3. Player 1 can continue as long as desired or until the sum of the number cubes is eight. If the sum is eight, the player loses all points for that round. If the player stops before getting a sum of eight, the players record the total of all points for the round. 4. Player 2 does the same. 5. Both players use the chart to keep a running total of points. 6. The player with the most points at the end wins!
*Probability of Compound Events *Review: A Simple Event has only one outcome. *New Info: A Compound Event is a combination of at least two simple events. *There are two kinds of compound events: 1. Independent Events - When the outcome of the first event has no influence on the likelihood of a future event occurring. 2. Dependent Events - When the outcome of the first event reduces the amount of possible outcomes (and as a result, the likelihood) of future event(s).
*Review of a Simple Event What is the probability of rolling less than a 5?
*Compound Events *To determine the probability of a compound event, multiply the probabilities of the individual events. Example: What is the probability of drawing a Queen and then a King? There are 52 cards in a deck and in it are 4 Queens as well as 4 Kings. So the odds are 4/52 (simplified to 1/13)
Probability of a single event Probability of the compound event *1/13 = 0.063 *(about six hundredths) *1/169 = 0.0059 *(about six thousandths) This one is less than 1/10 of this one! *Key Difference!
*Spinner Probability *A fair spinner is one on which all the sections are the same size. *A fair competition is one in which everyone has the same probability of winning. *To win, you must first spin a number higher than 7, and then then spin an even number. *Your probability
*Dependent Events *Abbreviations are used to illustrate what happens when we solve probabilities. P: Means total probability A: Refers to the first event B: Refers to the second event *Probability that 2 independent events will take place: P(A&B) = P(A) P(B) The probability of A and B both happening equals the probability of A times the probability of B. *Probability that 2 dependent events will take place: P(A&B) + P(A) P (B following A) The probability of A & B happening equals the probability of A times the probability of B after A has happened.
*Dependent Events * Example: You share your last jelly beans with a friend. *There are 12 jelly beans left over. *Both of you like the red beans most. There are only 2. *Your friend is next get to take two beans. *What is the probability that she can get both red beans? Note the pattern: P(A&B) = P(A) P(B following A)
*Practice *There are 12 marbles in the bag: 2 Blue 3 Yellow 3 Green 4 Red *Your friend is to reach in and try to take out a yellow marble. He will keep it out. You will try to the same with a red marble. What is the probability of success?
*Lucky Lottery *You will pick out three numbers between 1 and 30. *You may only use a number once. *If you pick the three winning numbers I have pre- selected, you will win the Grand Prize. *But, in order to submit your numbers and compete, you must also determine in writing the probability of winning. *You have 3 minutes to choose your numbers and figure out the probability. Do Not Click Again until ready to reveal probability
