You are at a game where you flip a fair coin (so Heads and Tails are equally lik

Question

You are at a game where you flip a fair coin (so Heads and Tails are equally likely). If bet $x. If Heads comes up, you 'get $0.9x: if Tails comes up, you lose the $x. You have $10,000, and you need to win at least $5,000 by tomorrow morning. a. Compute the likelihood of winning at least $5000 by making a single bet. b. Compute the likelihood of winning at least $1000 by playing the game 10,0000 times and betting a dollar each time. What is the likelihood of not losing money? Suppose a pdf f(x) is zero for x 1. Suppose a game is played where the random variable X(x) = x specifies the outcome. If the game is played 100 times, find the likelihood that the sum of the numbers is between 0 and 50.

Explanation / Answer

7

a.

Probability of coming Head=0.5

Amount got for a head for this bet $0.9X

Obtained amont=$5000

If probability of obtaining $5000 is Y

0.5*(0.9*10000*Y)+10000*0.5*Y=5000

Answer=52.63%

b.

0.5*0.9*(103 +1)Z+(103 +1)*0.5Z=1000

Answer=40.2%

8.

40%

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