Suppose you are playing a friendly game of Mario Kart with three of your younger

Question

Suppose you are playing a friendly game of Mario Kart with three of your younger cousins (four players total). Mario Kart is a racing game in which the winner is the person who finishes the race before everyone else.

Q1. What is the probability that you and your favorite cousin finish first and second? Here, whoever finishes first or second does not matter as long as it is either you or your favorite cousin. Assign your answer to a variable called first_and_second.

Now let's make this more realistic. Since your cousins are much younger and not nearly as skilled as you, say that the probability that you win a game is 0.97 and the chance that each of your younger cousins wins is 0.01.

Q2. How many games do you have to play before the probability of you winning all of them is below 75%? Assign your answer to a variable called win_all. Note that your answer should be a whole number.

Q3. If one of your younger cousins miraculously wins the first three games, what is the probability that this same cousin will win the 4th game? Assign your answer to a variable called prob_cousin_wins.

Explanation / Answer

QUestion 1. Here if p is the winning probability of me and my favourite cousin

Pr(Me and my favourite cousin comes first and second) = Pr(I come first) * Pr(He come second) + Pr(I come second) * Pr(He comes first)

Question 2

If number of such games are n then

Here Pr(All will win all) = BIN(n ; n; 0.97) < 0.75

nCn (0.97)n (0.03)0 < 0.75

n ln (0.97) < ln (0.75)

n < ln(0.75)/ ln(0.97) = 9.4448

so n is 10 here .

Question 3

As one of my younger cousins miraculously wins the first three games, that will not change the probability of same cousin winning the 4th game.

Pr(same cousin will win the game) = 0.01

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