1. A particular event has a probability of occurrence of p=0.65.Given 12 independent trials, draw the probability distribution and calculate the expected value.
2. A particular event has a probability of occurrence of p=0.65. If each outcome is independent of the last, draw the probability distribution associated with the event not occurring a given number of consecutive times and calculate the expected value.
3. Given the following scenario, determine which distribution (binomial, geometric, hypergeometric) is the most appropriate to model it? Rank the distributions from most appropriate to least appropriate. Explain the reason(s)."1600 students attend BOSS. It is determined that 70% of all BOSS students wear glasses. If groups of 50 students were selected at random, how many of them would be wearing glasses?"
4. In an earlier poll, it was determined that 55% of the population support the prime minister. Today, 100 people were polled and 50% of respondents approve. If these polls are conducted weekly, can one claim that the prime minister's popularity has decreased? Explain your thinking with the help of appropriate calculations.
5. Research on a new medication shows it is 85% effective in relieving allergy symptoms. In other words, 85 in 100 people would report feeling better a day after taking the drug. How many users of the medication would have to be surveyed before being 99.9% sure that at least someone felt relief?
6. Calculate and explain.

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