CSCI 246 Class 18 PROBABILITIES AND COUNTING Quiz Questions - PowerPoint PPT Presentation

CSCI 246 – Class 18 PROBABILITIES AND COUNTING

Quiz Questions  Lecture 30:  What is the probability of flipping one heads and one tails when flipping two fair coins?  Lecture 31:  Give the permutations for n = 3  Note, I’m not asking for the number of permutations

Notes and Clarifications  Finishing remarks from Friday:  elance.com  udacity.com  Project Question  Grades  Quiz

Lessons 30 and 31  Probability  Sample Space S 1  Probabilities: 0 < P(x) < 1; 𝑄 𝑦 = |𝑡| |𝐹|  𝑄 𝐹𝑤𝑓𝑜𝑢 = |𝑡|

Lessons 30 and 31  Probability  Monty Hall Game: https://www.youtube.com/watch?v=mhlc7peGlGg

Lessons 30 and 31  Multiplication Rule  The probability of event A and event B occurring (assuming independence of each other) = P(A) * P(B)  Example: Dice

Lessons 30 and 31  Permutation  Say we have 3 chairs and 7 people, what are the number of possible ways to seat these people?  Notation notes: 𝟖 𝑸 𝟒 , 𝑸 𝟒 𝟖 , 𝑸(𝟒, 𝟖)

Lessons 30 and 31  Rule of Addition  When two events, A and B, are mutually exclusive, the probability that A or B will occur is the sum of the probability of each event. P(A or B) = P(A) + P(B) Example: A glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. If a single marble is chosen at random from the jar, what is the probability that it is yellow or green?

Homework (group) Assuming a standard playing deck of 4 suits, each with 13 cards, what is the probability of 1. getting a jack? P(jack) = ? Assuming a standard playing deck of 4 suits, each with 13 cards, what is the probability of 2. getting a jack that is also a heart? P(jack AND heart) = ? Assuming a standard playing deck of 4 suits, each with 13 cards, what is the probability of 3. getting a jack or a heart? P(jack OR a heart) = ? Assume you have 13 people and 5 chairs, what are the total possible ways for people to sit in 4. those chairs? What is the probability of rolling a 4 on the first roll and an even number on the second role 5. when using a fair dice? A spinner has 4 equal sectors colored yellow, blue, green, and red. What is the probability of 6. landing on red or blue after spinning this spinner?

Homework (individual) If a dice is rolled once, what is the probability that it will show a prime number ( 1 is not prime) 1. If a coin is flipped twice, what is the probability that it will land heads at least once? 2. Which of these numbers cannot be a probability? 3. a) -0.00001 b) 0.5 c) 1.001 d) 0 e) 1 f) 20% What are the total number of permutations for 7 people to sit in 7 chairs? 4.