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A company has 15 employees. Four are managers, six are engineers, and five are interns. In how many ways can the company select a CEO, a CFO, and a COO, given that only a manager can be the CEO, and the other two positions can be filled by any employee, with no one holding more than one position

An article in The Journal of Data Science [“A Statistical Analysis of Well Failures in Baltimore County” (2009, Vol. 7, pp. 111-127)] provided the following table of well failures for different geological formation groups in Baltimore County.    Geological Formation Group Wells Failed Wells Total Gneiss 170 1685 Granite 2 28 Loch raven schist 443 3733 Mafic 14 363 Marble 29 309 Prettyboy schist 60 1403 Other schists 46 933 Serpentine 3 39   Let A denote the event that the geological formation has more than 1000 wells, and let B denote the event that a well failed. Determine the number of wells in each of the following events.   Find the following, P(A Bc)  

Suppose that a 12% discount is independently applied to online orders for electronics with a probability of 0.2. What is the probability that the first discount is applied to the fourth order?

A bag contains 4 red balls and 6 blue balls. Two balls are drawn at random (without replacement). What is the probability that both balls drawn are of the same color?

Mary and Mark draw 13 cards each from a standard deck of 52. Given that Mary has exactly two Queens, What is the probability that Mark has exactly one Queen?   (Assume that, all cards were chosen randomly without replacement and Mary picks her cards first then Mark picks after).

50 high school seniors were asked about their plans following graduation. 30 students planned to attend college.  14 planned to attend only an in-state college. 11 planned to attend only an out-of-state college. 8 did not plan to attend college 12 were undecided. What percent of this group of seniors is not planning to attend an in-state-college?

Consider the data on wafers classified by contamination and location in the table below.   Number of Contamination Particles Center Edge Totals 0 0.28 0.12 0.40 1 0.17 0.03 0.20 2 0.1 0.05 0.15 3 0.06 0.04 0.10 4 0.04 0.01 0.05 5 or more 0.07 0.03 0.10 Totals 0.72 0.28 1   Assume that one wafer is selected at random from this set. Let A denote the event that a wafer contains four or more particles, and let B denote the event that a wafer is from the center of the sputtering tool. Determine P(B|A) 

An bag contains 15 marbles of which 10 are red and 5 are white. 5 marbles are selected from the bag. How many samples (of size 5) have at most 2 red marbles?

Consider the following circuits of 4 identical relays. The probability that any relay works is 0.7 and the failures of the relays are independent. What is the probability that, when current is applied, it flows from point 1 to 2?    

A game at a carnival involves rolling a fair six-sided die. The payouts are as follows: If you roll a 6, you win $10. If you roll a 4 or 5, you win $5. If you roll a 1, 2, or 3, you win nothing ($0$). What is the expected payout per roll (i.e. Find the expected value) ?