- Quiz 4 Practice Problems 1 You Are Given An Event E And Another Event F That Satisfy The Following Conditions P E 0 1 (154.47 KiB) Viewed 73 times
- Quiz 4 Practice Problems 1 You Are Given An Event E And Another Event F That Satisfy The Following Conditions P E 0 2 (51.95 KiB) Viewed 73 times
Quiz 4 Practice Problems 1. You are given an event E and another event F that satisfy the following conditions: P(E) = 0.65, P(F) = 0.32, and P(E|F) = 0.24. Calculate: (i) P(E and F), (ii) P(E or F) 2. The random variable X for this
question is X = Number of years it takes to earn a Bachelor of Science (B.S.) degree The table below gives the probability distribution for X 3 4 5 6 4 PC) 0.05 0.40 0.30 0.15 0.10 (a) On average, how long, in years, an individual expect to take to earn a B.S.? (b) What is the standard deviation for this distribution? 3. A venture capitalist, willing to invest $1000000, has three investments to choose from. The first investment, a software
company, has a 10% chance of returning $5000000 profit, a 30% chance of returning $1000000 profit, and a 60% chance of losing the million dollars. The second
company, a hardware
company, has a 20% chance of returning $3000000 profit, a 40% chance of returning $1000000 profit, and a 40% chance of losing the million dollars. The third
company, a biotech firm, has a 10% chance of returning $6000000 profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars. Take the random variable X for this problem to be X = Return on investment when $1000000 is invested in
company (a) Construct a probability distribution of X for each investment. (b) Find the expected value for each investment. (c) Which is the safest investment? Why do you think so? (d) Which is the riskiest investment? Why do you think so? (e) Which investment has the highest expected return, on average? 4. The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. Of those surveyed, 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick five first-time, full-time freshmen from the survey and ask them whether or not they believe that same-sex couples should have the right to legal marital status. (a) Explain why this is a binomial experiment. (b) What is the random variable X for this experiment? (c) Construct the probability distribution for X. (d) What is the probability that at most two freshmen will answer yes? 1
5. A student takes a 12-
question multiple-choice exam but did not study and randomly guesses each answer. Each
question has three equally possible choices for the answer. (a) Explain why this is a binomial activity. 1 (b) Explain why the probability of a YES is 3 (c) To pass the exam, the student must answer at least 75% of the
questions correctly. Find the probability that he/she will pass the exam. 2