Let us assume that the game company has designed a guarantee mechanism to encourageusers to pay for the card. The idea is simple. We randomly shuffled 3 Thanos, 5 Thor, 5Iron 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 cardsone by one. What is the average probability of getting at least one "Thanos" in thefirst 30 draws?2. How much higher is the probability of getting at least one "Thanos" in the first 30draws under our guarantee mechanism than without the guarantee? (3. Using the same method, we draw 100 cards and simulate the following probabilitiesfor j = 1,.,98:%3DP (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 1to 100, and on the y-axis, you show the corresponding probabilities.4. What is the theoretical value ofP (Thanos appears at 96th draw Thanos never appeared once in the previous 95 draws.)?Check the simulated value with the theoretical one.

Note :- as per bartleby guidlines i have solved part off first part only. Please post again if u…

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?