# What is the probability that he found his dog alive 4

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on the fourth day. What is the probability that he found his dog alive? 4) In the small town ABC by the Aegean cost of Turkey, daily weather statistics of April are given below: it is rainy for 25%, partly cloudy for 35 %, and sunny for 40 % of April. a) Find the probability of exactly 10 sunny days in April, in ABC? b) For 10 years duration, what is the probability that for exactly 4 years, we have exactly 10 sunny days in April (in a year) in that town? c) What is the probability of exactly 10 sunny and 8 rainy days in April in ABC? 5) Students arrive at the EA building at random times between 10:10 and 10:40. Each arriving student is an EE230 student with probability p, independently of all other students. Let X be the total number of EE230 students among the first 50 students that arrive. a) Express X as a sum of 50 Bernoulli random variables. b) Compute the Probability Mass Function (PMF) of X. c) Make a rough sketch of the PMF in (b). d) Express the probability that at least half the students are EE230 students, in terms of the PMF in (b). e) Gele Bilir is an EE230 student. Given that Gele is the 20 th student to arrive, what is the probability that he is the 10 th EE230 student to arrive?
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