Section 4 3 Events of Fixed Length

Section 4. 3 Events of Fixed Length

“The Birth Month Game” Assume that birthdays are spread randomly throughout the year Choose X people in Hawk Hall If at least 2 of them were born in the same month, the “house” (that’s me) wins If not, those X people win Vote on # people to be chosen 4. 3 Events of Fixed Length

Play (for real $) 1. 2. 4. 3 Events of Fixed Length 3. 3

Birth Month 1. Name of Problem: 2. Outcomes whose probabilities we know: 3. Rand. Int( 4. ( 5. Answer: , , ) . Random integer correspondences: Vote Trials): “Mathematical” Answer 4. 3 Events of Fixed Length 4

Common Mistake in “Birth Month” 2. Outcomes whose probabilities we know: Random integer correspondences: Match No Match Why? 4. 3 Events of Fixed Length

“All That Jazz” Wesley asks 7 fellow musicians to join his group There is a 50% chance that any one of them will say “yes” He needs at least 4 of them to get the sound he wants What are the chances Wesley forms his group? All that Jazz 4. 3 Events of Fixed Length 6

1. Name of Problem: 2. Outcomes whose probabilities we know: 3. Rand. Int( 4. ( 5. Answer: , , . ) Random integer correspondences: Vote Trials): 4. 3 Events of Fixed Length 7

Common Mistake in “All that Jazz” 2. Outcomes whose probabilities we know: Random integer correspondences: Forms the group Doesn’t form the group Why? 4. 3 Events of Fixed Length

“Free Throw Shooting (2 Shots)” Erica makes 2/3 of her free-throws Near the end of a game she takes 2 free throws Animation So Erica can score either 0 or 1 or 2 points. Which is most likely? 4. 3 Events of Fixed Length

1. Name of Problem: 2. Outcomes whose probabilities we know: 3. Rand. Int( 4. ( 5. Answer: , , . ) Random integer correspondences: Vote Trials): 4. 3 Events of Fixed Length 10

What numbers would we use if Erica made a free throw 3/4 of the time? Make it Miss it 9/10 of the time? Make it Miss it 45% of the time? Make it Miss it 4. 3 Events of Fixed Length 11

1 … 2 … 3 … 4 … 5 … 6 “The Exam” … You feel you have an 80% chance to answer any single question on a math test correctly. The test has 6 questions What are the chances that you get a perfect score? 4. 3 Events of Fixed Length

1. Name of Problem: 2. Outcomes whose probabilities we know: 3. Rand. Int( 4. ( 5. Answer: , , . ) Random integer correspondences: Vote Trials): 4. 3 Events of Fixed Length 13

“Dice 7 -11” Two dice are tossed. What are the chances that the sum of the numbers coming up is 7 or 11? 4. 3 Events of Fixed Length

1. Name of Problem: 2. Outcomes whose probabilities we know: 3. Rand. Int( 4. ( 5. . Random integer correspondences: Vote Answer: , , ) Trials): 4. 3 Events of Fixed Length 15

“Job Discrimination” Three sales positions are open. 10 men and 15 women apply. All are equally qualified. After the interviews all three positions go to men. The women complain of gender discrimination. Do they have a case? 4. 3 Events of Fixed Length

1. Name of Problem: 2. Outcomes whose probabilities we know: 3. Rand. Int( 4. ( 5. . Random integer correspondences: Vote Answer: , , ) Trials): 4. 3 Events of Fixed Length 17

“Traffic Lights” Animation There are two stoplights on Bloomfield Ave. Each is • Red • Green • Yellow light) 9/15 of the time 4/15 of the time 2/15 of the time (Let’s assume you stop on a yellow What are the chances that you stop at both lights? 4. 3 Events of Fixed Length

1. Name of Problem: 2. Outcomes whose probabilities we know: 3. Rand. Int( 4. ( 5. Answer: , , . ) Random integer correspondences: Vote Trials): 4. 3 Events of Fixed Length 19

“Scissors, Rock, Paper” There are three players who simultaneously flash one of their hands in one of three ways: Scissors, Rock or Paper Player A wins if all three hands are the same Player B wins if all three hands are different Player C wins if exactly two of the hands are the same Who wins the game? 4. 3 Events of Fixed Length

1. Name of Problem: 2. Outcomes whose probabilities we know: 3. Rand. Int( 4. ( 5. Answer: , , . ) Random integer correspondences: Vote Trials): 4. 3 Events of Fixed Length 21

“Hi - Lo” Player A tosses a die. Player B then tosses another die. If Player B’s number is higher than player A’s number, B wins. Otherwise, A wins. Who has the better chance of winning this game? 4. 3 Events of Fixed Length

1. Name of Problem: 2. Outcomes whose probabilities we know: 3. Rand. Int( 4. ( 5. Answer: , , . ) Random integer correspondences: Vote Trials): 4. 3 Events of Fixed Length 23

“Heads on Third Toss” Suppose that you toss a coin twice and get two HEADS. What are the chances that you will get a HEAD on the next toss? 1. 50% 2. Less than 50% 3. More than 50% Vote here first then calculate on next slide 4. 3 Events of Fixed Length 24

1. Name of Problem: . 2. Outcomes whose probabilities we know: Random integer correspondences: 3. Rand. Int( 4. ( 5. Answer: , , ) Trials): Re-Vote 4. 3 Events of Fixed Length 25

“One Head or Two”? You toss a coin 3 times. The chances of getting exactly 1 head are same as getting 2 heads 1. True 2. False Vote here first then calculate on next slide 4. 3 Events of Fixed Length

1. Name of Problem: . 2. Outcomes whose probabilities we know: Random integer correspondences: 3. Rand. Int( 4. ( 5. Answer: , , ) Trials): Re-vote 4. 3 Events of Fixed Length 27

End of 4. 3 Events of Fixed Length 28

Advise me. How many people should we choose to play the game? Be sure to have a plausible reason. 1. 4 or fewer 2. 5 3. 6 4. 7 5. 8 6. 9 or more 4. 3 Events of Fixed Length

“Birth Month” - What's the best choice? 1. Rand. Int(1, 2, ) 2. Rand. Int(1, 2, 12) 3. Rand. Int(1, , 2) 4. Rand. Int(1, , 12) 5. Rand. Int(1, 12, ) 6. Rand. Int(1, 12, 2) 7. None of the above 4. 3 Events of Fixed Length

“All That Jazz” I’m in Love to, but can’t right now You up for it? You in? How about you? Sure Wesley 4. 3 Events of Fixed Length

Chances that the “house” (me) loses = No matches Therefore, We win % of the time 4. 3 Events of Fixed Length

“All that Jazz” - What's the best choice? 1. Rand. Int(1, 2, 2) 2. Rand. Int(1, 2, 7) 3. Rand. Int(1, 4, 2) 4. Rand. Int(1, 4, 7) 5. Rand. Int(1, 7, 2) 6. Rand. Int(1, 7, 7) 7. None of the above 4. 3 Events of Fixed Length

Swish! 4. 3 Events of Fixed Length 34

Swish! 2 Points 4. 3 Events of Fixed Length 35

Clank! 4. 3 Events of Fixed Length 36

Swish! 1 Point 4. 3 Events of Fixed Length 37

Clank! 4. 3 Events of Fixed Length 38

Clank! 0 Points 4. 3 Events of Fixed Length 39

“ 2 -Shot Free Throw” What's the best choice? 1. Rand. Int(1, 2, 1) 2. Rand. Int(1, 2, 2) 3. Rand. Int(1, 2, 3) 4. Rand. Int(1, 3, 1) 5. Rand. Int(1, 3, 2) 6. Rand. Int(1, 3, 3) 7. None of the above 4. 3 Events of Fixed Length

“The Exam” - What's the best choice? 1. Rand. Int(1, 5, 6) 2. Rand. Int(1, 6, 5) 3. Rand. Int(1, 80, 6) 4. Rand. Int(1, 100, 6) 5. None of the above 4. 3 Events of Fixed Length

“Dice 7/11” - What's the best choice? 1. Rand. Int(1, 6, 2) 2. Rand. Int(1, 7, 2) 3. Rand. Int(1, 11, 2) 4. Rand. Int(1, 12, 2) 5. Rand. Int(1, 36, 2) 6. None of the above 4. 3 Events of Fixed Length

Arggggh! I hit ‘em both, as usual 4. 3 Events of Fixed Length 43

“Job Discrimination” - What's the best choice? 1. Rand. Int(1, 3, 3) 2. Rand. Int(1, 10, 3) 3. Rand. Int(1, 15, 3) 4. Rand. Int(1, 25, 3) 5. None of the above 4. 3 Events of Fixed Length

“Traffic Lights” - What's the best choice? 1. Rand. Int(1, 4, 2) 2. Rand. Int(1, 9, 2) 3. Rand. Int(1, 10, 2) 4. Rand. Int(1, 15, 2) 5. None of the above 4. 3 Events of Fixed Length

“Rock, Scissors, Paper” What's the best choice? 1. Rand. Int(1, 2, 3) 2. Rand. Int(1, 3, 3) 3. Rand. Int(1, 6, 3) 4. Rand. Int(1, 27, 3) 5. None of the above 4. 3 Events of Fixed Length

“Hi – Lo” - What's the best choice? 1. Rand. Int(1, 5, 2) 2. Rand. Int(1, 6, 2) 3. Rand. Int(1, 12, 2) 4. Rand. Int(1, 36, 2) 5. None of the above 4. 3 Events of Fixed Length

Meta - Material 4. 3 Events of Fixed Length 48