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Let us assume that the game company has designed a guarantee mechanism to encourage users to pay for the card. The idea is simple. We randomly shuffled 3 Thanos, 5 Thor, 5 Iron Man, 29 Hulk, 29 Captain America, and 29 Loki cards into the pool. 1. We simulate 1000 times the following situation: shuffle the deck and draw 100 cards one by one. What is the average probability of getting at least one "Thanos" in the first 30 draws?

Let us assume that the game company has designed a guarantee mechanism to encourage users to pay for the card. The idea is simple. We randomly shuffled 3 Thanos, 5 Thor, 5 Iron Man, 29 Hulk, 29 Captain America, and 29 Loki cards into the pool. 1. We simulate 1000 times the following situation: shuffle the deck and draw 100 cards one by one. What is the average probability of getting at least one "Thanos" in the first 30 draws?

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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Let us assume that the game company has designed a guarantee mechanism to encourage users to pay for the card. The idea is simple. We randomly shuffled 3 Thanos, 5 Thor, 5 Iron Man, 29 Hulk, 29 Captain America, and 29 Loki cards into the pool. 1. We simulate 1000 times the following situation: shuffle the deck and draw 100 cards one by one. What is the average probability of getting at least one "Thanos" in the first 30 draws? 2. How much higher is the probability of getting at least one "Thanos" in the first 30 draws under our guarantee mechanism than without the guarantee? ( 3. Using the same method, we draw 100 cards and simulate the following probabilities for j = 1,.,98: %3D P (Thanos appears at jth draw Thanos never appeared once in the previous j-1 draws.). make a plot to show the curve of probabilities, where on the x-axis you put j from 1 to 100, and on the y-axis, you show the corresponding probabilities. 4. What is the theoretical value of P (Thanos appears at 96th draw Thanos never appeared once in the previous 95 draws.)? Check the simulated value with the theoretical one.
Transcribed Image Text:Let us assume that the game company has designed a guarantee mechanism to encourage users to pay for the card. The idea is simple. We randomly shuffled 3 Thanos, 5 Thor, 5 Iron Man, 29 Hulk, 29 Captain America, and 29 Loki cards into the pool. 1. We simulate 1000 times the following situation: shuffle the deck and draw 100 cards one by one. What is the average probability of getting at least one "Thanos" in the first 30 draws? 2. How much higher is the probability of getting at least one "Thanos" in the first 30 draws under our guarantee mechanism than without the guarantee? ( 3. Using the same method, we draw 100 cards and simulate the following probabilities for j = 1,.,98: %3D P (Thanos appears at jth draw Thanos never appeared once in the previous j-1 draws.). make a plot to show the curve of probabilities, where on the x-axis you put j from 1 to 100, and on the y-axis, you show the corresponding probabilities. 4. What is the theoretical value of P (Thanos appears at 96th draw Thanos never appeared once in the previous 95 draws.)? Check the simulated value with the theoretical one.
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