Question

PIUBlem 2. The Video Game Question. When I am not grading the ridiculous amounts of game. Let's talk statistics of digital card games. exams I have this semester, I play a digital card a) According to a website that tracks statistics, the deck I currently am playing has a 63% win-rate. It 1 plan to play 10 games tonight before I start grading, what is the probability that I win 8 or more of them? b) Rather than play a specified number of games, I instead decide to keep playing until I lose my 3rd game. I'm using the same deck with a 63% win rate. What is the probability that I play 10 or more games? c) There is 1 card in my deck that is quite powerful and I want to play it on turn 3. The deck consists of 30 cards with 1 copy of the powerful card. Initially 3 cards are drawn and one has the option to return some or all of them for new draws (the cards are shuffled back in the deck after replacements are drawn.) Additionally, a card is drawn each turn. What is the probability that I will have the powerful card by turn 3? (3 cards in starting hand and then 3 drawn cards.)

Answer 1

a)
X follow binomial distribution with n = 10 , p= 0.63
P(X >= 8)
= P(X = 8) + P(X = 9) + P(X = 10)
= 0.22057

b)
X follow negative binomial distribution with r = 3
p = 1 - 0.63 = 0.37
P(X >= 10)
= 1 - P(X<= 9)
= 1 - 0.7076
= 0.2924