please help me with probability and statistics homework Alex plays a game in a c
ID: 3306776 • Letter: P
Question
please help me with probability and statistics homework
Alex plays a game in a casino. Each time he plays, he wins with probability 3% (independent of other trials). He should pay $ 5 For each game he wants to play, but he gets $ 100 whenever wins (a) What is the probability that he plays 10 times without any win (b) Alex decided to keep playing until he wins, and just leave the casino with his S 100. What is the probability he ends up playing exactly 8 games? (c) Use MATLAB command geopdf to compute the probability in part (b). Hint: Note that this command with inputs geopdf (k, p) computes the probability of k failures and 1 success, i.e, (1-p p. Hence to get the answer for part (b) you should use geopdE (7, 0.03). (d) Assume Alex has only $20 when he enters the casino, so he can play at most 4 games without winning. What is the probability that he can play 5 games or more? (e) Use MATLAB command geocdf to compute this probability.Explanation / Answer
a) probability of winning = p = 0.03
probability of not winning = 1- p= 0.97
probability of playing 10 games without win = 0.97^10 = 0.73742
b) P(first win in 8th game) = 0.97^7 * 0.03 = 0.024239
c)
geopdf(7,0.03)
ans =
0.0242
d)
Probability of playing 5 or more games = 1 - probability of loosing all 4 games
= 1- 0.97^4
= 0.1147071
e)
geocdf(3,0.03)
ans =
0.1147
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