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1. Kunal and Liying play a game in which Kunal flips 2 fair coifis, each outcome of the game as a pair (K, L) where K is the number of heads Kunal gets, and L is the number of heads Liying gets. If Liying flips more heads than Kunal (or K L), then Liying has to give Kunal $4. If they both flip the same number of heads (or K= L), then Liying has to give Kunal $1. For example, the outcome (2, 1) means that Kunal flipped two heads and Liying flipped one (K > L), so Liying would pay $4 to Kunal. (i) Consider the event that Liying flips more heads than Kunal, or K

1. Kunal and Liying play a game in which Kunal flips 2 fair coifis, each outcome of the game as a pair (K, L) where K is the number of heads Kunal gets, and L is the number of heads Liying gets. If Liying flips more heads than Kunal (or K L), then Liying has to give Kunal $4. If they both flip the same number of heads (or K= L), then Liying has to give Kunal $1. For example, the outcome (2, 1) means that Kunal flipped two heads and Liying flipped one (K > L), so Liying would pay $4 to Kunal. (i) Consider the event that Liying flips more heads than Kunal, or K

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1. Kunal and Liying play a game in which Kunal flips 2 fair coins, and Liying flips 3 fair coins. Represent each outcome of the game as a pair (K, L) where K is the number of heads Kunal gets, and L is the number of heads Liying gets. • If Liying flips more heads than Kunal (or K<L), then Kunal has to give Liying $2. If Kunal flips more heads than Liying (or K> L), then Liying has to give Kunal $4. If they both flip the same number of heads (or K= L), then Liying has to give Kunal $1. For example, the outcome (2, 1) means that Kunal flipped two heads and Liying flipped one (K> L), so Liying would pay $4 to Kunal. (i) Consider the event that Liying flips more heads than Kunal, or K<L. Explicitly write out all outcomes where K<L. (Your answer should be a set consisting of ordered pairs.) (ii) Compute the probability that Kunal flipped fewer heads than Liying, or P(K<L). (iii) Compute the probability that Kunal flipped two heads, given that Kunal lost money.
Transcribed Image Text:1. Kunal and Liying play a game in which Kunal flips 2 fair coins, and Liying flips 3 fair coins. Represent each outcome of the game as a pair (K, L) where K is the number of heads Kunal gets, and L is the number of heads Liying gets. • If Liying flips more heads than Kunal (or K<L), then Kunal has to give Liying $2. If Kunal flips more heads than Liying (or K> L), then Liying has to give Kunal $4. If they both flip the same number of heads (or K= L), then Liying has to give Kunal $1. For example, the outcome (2, 1) means that Kunal flipped two heads and Liying flipped one (K> L), so Liying would pay $4 to Kunal. (i) Consider the event that Liying flips more heads than Kunal, or K<L. Explicitly write out all outcomes where K<L. (Your answer should be a set consisting of ordered pairs.) (ii) Compute the probability that Kunal flipped fewer heads than Liying, or P(K<L). (iii) Compute the probability that Kunal flipped two heads, given that Kunal lost money.
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