You are buying a stock today, and intend to hold it for 7 days. The stock prices change every day, and it has an equal chance to go up or down (they are equally likely outcomes). 

Questions: a- What is the probability that the stock price will move up 2 times (days) during the holding period? What type of distributions applies to this example? Please explain your answer. 

b- If the investor is very optimistic that the stock price will move up with a 65% chance. What is the distribution that you will use in this case (explain your answer)? And what is the probability that the stock will move up at least one time (day) during the holding period? 

c- In case you have a portfolio of 20 stocks which includes many low-rating companies stocks, and the expected number of stocks going bankrupt is 4.7 per month. What is the probability of having 10 bankrupt stocks over the coming four months?