Consider a roulette wheel consisting of 38 numbers 1 through 36, 0, and double 0

boitshupoO

boitshupoO

Answered question

2021-11-09

Consider a roulette wheel consisting of 38 numbers 1 through 36, 0, and double 0. If Smith always bets that the outcome will be one of the numbers 1 through 12, what is the probability that (a) Smith will lose his first 5 bets; (b) his first win will occur on his fourth bet?

Answer & Explanation

Derrick

Derrick

Skilled2021-11-10Added 94 answers

a) Observe that the probability that he loses a single bet is simply 26/38 so, because of the independence, the probability that he loses all his five betting is
(2638)5=0.15
b) Define random variable Y that marks the first time that he wins a bet. From the nature of the problem we know that Y Geom (1238). So, the requred probability is simplify
P(Y=4)=(2638)31238=0.101
a) 0.15, b) 0.101

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