Campos Martinez
10/28/2023 · Junior High School
4) If \( \left[\Omega, \mathscr{A}=2^{\Omega}, P\right] \) is a probability space of tossing three identical fair coins at the same time. Then: a) Determine \( \Omega \) and \( P \) for this random experiment. b) Calculate the probability of getting one or two heads. c) If we know that we had at least one tail, what is the probability that we have two tails ?
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a) \(\Omega = \{ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \}\), \(P(A) = \frac{|A|}{8}\)
b) \(P(\text{one or two heads}) = \frac{3}{4}\)
c) \(P(\text{two tails} \mid \text{at least one tail}) = \frac{3}{7}\)
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