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- 1. A beverage manufacturing company uses a pair of redundant pumps to transfer flavored syrups to the bottling line. Each pump has a À of 0.055 failures per year and ß of 0.05. What is the probability that both pumps will fail during a 45 day production run? a. 0.00004 b. 0.00034 c. 0.00038 d. 0.124.Suppose we begin with a population of normally distributed values with mean zero and S.D. = 1 and we add a positive number k to every value. If a value is randomly selected from this population, find the probability that it is greater than k + 1.
- Q. 1 It is estimated that 70% of emails are spam emails. Some software has been applied to filter these spam emails before they reach our inbox. A certain brand of software claims that it can detect 99% of spam emails, and the probability for a false positive (a non-spam email detected as spam) is 5%. Now if an email is detected as spam, then what is the probability that it is in fact a non-spam email?1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.Suppose that the rats on the campus of Hypothetical U are found to be carriers of bubonic plague. Eradicating the rats has an estimated cost of $1,000,000 and is expected to reduce the probability a given student dies of the plague from 1/3,000 to zero. Suppose that there are 30,000 students on campus. Suppose further that the administration refuses to eradicate the rats due to the cost. From this information, we can estimate that the administration's willingness to pay to save a student statistical life is no more than $100,000 $1,000,000 $50,000 $33,333
- Determine whether the event described are independent or dependent. Then find the probability of the event Randomly drawing and immediately eating three red M&Ms in a row from a bag that contains 10 red M&Ms out of 30 M&Ms totalAssume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .Q. 1 It is estimated that 80% of emails are spam emails. Some software has been applied to filter these spam emails before they reach our inbox. A certain brand of software claims that it can detect 99% of spam emails, and the probability for a false positive (a non-spam email detected as spam) is 5%. Now if an email is detected as spam, then what is the probability that it is in fact a non-spam email? event A: email is spam; event B: email is detected as spam. Assume that
- A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.95 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes. (a) Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state? Note that this result is the probability of being in the delay state for two consecutive periods. = (b) What is the probability that in the long run the traffic will not be in the delay state? (Enter your probabilities as fractions.) No Traffic Delay Traffic Delay π 1 =…5. A commuter must pass through 4 different traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below.X P(X) 0 0.05 1 0.25 2 0.35 3 0.20 4 0.15a. What is the probability she is stopped one time on her way to work?b. What is the probability she is stopped at least two times on her way to work
