1 / 16

Probability

Explore the Monty Hall Paradox from the old game show "Let's Make a Deal" and discuss the probability of switching or staying with your original choice. Learn about basic probability, set notation, mutually exclusive events, and independent and dependent events.

stacystone
Download Presentation

Probability

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Probability

  2. The Monty Hall Paradox • On the old game show “Let’s Make a Deal” a contestant is presented with 3 doors where only one of them hides a prize. • The contestant chooses a door, and Monty Hall (the host) then opens one of the unchosen doors that is empty. • He then offers the contestant a choice. They may stay with their original choice or switch to the other unopened door. • Should the contestant switch, stay with their first choice, or does it matter. • Discuss it with the person next to you and write on a piece of paper what your decision would be and prove that you’re right.

  3. Basic probability • Probability experiments always involve chance • Each repetition of the experiment is a trial • Each possible result is an outcome • A set of outcomes is an event • A set of all possible outcomes is a sample space

  4. Basic probability • Theoretical probability is how likely each outcome will happen. • What is the probability of rolling a 3 on a 6 sided die? • What is the probability of drawing a face card from a standard deck of playing cards? • When presented with 3 doors where only one has a new car behind it, what is the probability of choosing the one with the car?

  5. You chose door number 2, and Monty Hall opened door 3 and it was hiding a goat. Now he asks, “Do you want door number 2 or door number 1?” So should you stay or switch? What is the probability the car behind 2 What is the probability the car is behind 1? Are you sure?

  6. Also known as “OR” Also known as “AND” Also known as “NOT” Set Notation Set A: 1,2,3,4,5,6 Set B: 2,4,6,8 =1,2,3,4,5,6,8 • Union: Include everything in both sets. • Intersection: Include only the data that both sets have in common. • Complement: Include only the data not in the set. =2,4,6 =8 =1,3,5

  7. Set notation and probability • Your grocery basket contains one bag of each of the following items: oranges, green apples, green grapes, green broccoli, white cauliflower, orange carrots, and green spinach. You are getting ready to transfer your items from your cart to the conveyer belt for check-out. Event A is picking a bag containing a vegetable first. Event B is picking a bag containing a green food first. All bags have an equal chance of being picked first. • What is the probability of picking a green vegetable? • What is the probability of picking a fruit that is not green? What set notation represents that? What set notation represents that?

  8. More probability • You roll a pair of 6 sided dice at the same time. What is the probability that you do not roll a 7?

  9. 2 Way Table Blue Die • To make it less confusing, one die is blue and the other is green. • Which outcomes are we looking for? Green Die

  10. Example • One pile of cards contains the numbers 2 through 6 in red hearts. A second pile of cards contains the numbers 4 through 8 in black spades. Each pile of cards has been randomly shuffled. If one card from each pile is chosen at the same time, what is the probability that the sum will be less than 12?

  11. Mutually Exclusive • Events are mutually exclusive if they cannot both occur in the same trial • Ex: flip a coin heads or tails • Ex not mutually exclusive: deck of cards a club or a jack

  12. Probability with Mutually exclusive events • If events are mutually exclusive, then you add the probability • If they are not mutually exclusive, then add probability and subtract the probability of the overlapping events

  13. Example • If you roll a 12 sided die, what is the probability you roll an odd number or a multiple of 4 • What is the probability of rolling an even number or a multiple of 5?

  14. Independent and Dependent Events • Independent event: each outcome does NOT affect the next • Ex: flip 2 coins, outcomes are independent of each other • Dependent event: each outcome DOES affect the next • Ex: pick two cards, the second draw probability changes because there is one less card in the deck

  15. Probability of Independent Events • Multiply the probability for each event • Ex: roll 3 dice, what is the probability that the first 2 show 5 and the third is an even number. • A bag holds 9 dimes and 7 pennies, you randomly select one coin, put it backl and select another. What is the probability both were dimes

  16. Probability of Dependent Events • Similar to independent, still multiply probabilities • Just remember the probability changes after the first event so you have to calculate it again before multiplying. • Ex: 3 cards are dealt, what is the probability of drawing a heart, another heart, and a spade in that order?

More Related