Download presentation
Presentation is loading. Please wait.
Published byErnest Greer Modified over 5 years ago
1
Discrete Math for CS CMPSC 360 LECTURE 34 Last time:
Conditional probability. Bayesβ rule. Today: Total probability rule. CMPSC 360 8/2/2019
2
Conditional probability: definition
Let A and B be events, and suppose that Pr π΅ β 0. The conditional probability Pr π΄ π΅ , the probability of A given B, is Pr π΄ π΅ = Pr π΄β©π΅ Prβ‘[π΅] . 8/2/2019
3
Useful conditional probability facts
Bayesβ rule. Let A and B be events, and suppose that Pr π΅ β 0. Then Pr π΄ π΅ = Pr π΅|π΄ β
Pr π΄ Prβ‘[π΅] . Total probability rule. Let A and B be events. Then Pr π΅ = Pr π΅ π΄ β
Pr π΄ + Pr π΅ π΄ β
Pr π΄ . 8/2/2019
4
Clicker question (frequency BC)
Test for medical disorder (from last lecture/recitations). We choose a random person from the population. Event A: the chosen person is affected. Event B: the chosen person tests positive. Pr π΄ =0.05, Pr π΅ π΄ 0.9, Pr π΅ π΄ =0.2. What is the probability of A given that B occurred, Prβ‘[π΄|π΅]? < 0.1 In the interval [0.1,0.2). In the interval [0.2,0.3). In the interval [0.3,0.5). β₯0.5 8/2/2019
5
Tennis match You will play a tennis match against opponent X or Y. If X is chosen, you win with probability 0.7. If Y is chosen, you win with probability 0.3. Your opponent is chosen by flipping a coin with bias 0.6 in favor of X. What is your probability of winning? 8/2/2019
6
Clicker question (frequency BC)
You will play a tennis match against opponent X or Y. If X is chosen, you win with probability 0.7. If Y is chosen, you win with probability 0.3. Your opponent is chosen by flipping a coin with bias 0.6 in favor of X. What is your probability of winning? < 0.3 In the interval [0.3,0.4). In the interval [0.4,0.55). In the interval [0.55,0.7). β₯0.7 8/2/2019
7
Balls and bins We have two bins with balls.
Bin 1 contains 3 black balls and 2 white balls. Bin 2 contains 1 black ball and 1 white ball. We pick a bin uniformly at random. Then we pick a ball uniformly at random from that bin. What is the probability that we picked bin 1, given that we picked a white ball? 8/2/2019
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.