In the 17th century, the discipline of probability theory got its start when a gambler asked a mathematician friend to explain some observations about dice games. why did he, on average, lose a bet that at least one six would appear when rolling a die four times? and why did he seem to win a similar bet, getting at least one double six when rolling a pair of dice 24 times?

What is the proper adjusted cash balance per bank? (round answers to 2 decimal places, e.g. 52.75.) the proper adjusted cash balance per bank $enter a dollar amount rounded to 2 decimal places (b) what is the proper adjusted cash balance per books? (round answers to 2 decimal places, e.g. 52.75.) the proper adjusted cash balance per books

Prairie, inc. produces one single product. it has an annual capacity of 10,000 units, but currently uses only 80% of it. each unit is sold for $50 and requires direct material worth $30 and direct labor worth $5. manufacturing overhead cost is $10 per unit of which 70% is variable. should a special order to sell 1,000 units at $44 be accepted? yes no

Apharmaceutical packaging company (ppc) has decided to reorganize its processes into cells. the company has four different production operations, each requiring a unique piece of equipment. the names and functions of the four pieces of equipment are sort, count, place, and package. the company packages five different families of products (a, b, c, d, and e). the tables below indicate the demand (total units/day by product family), required operations, and operation cycle times for each product family. assume that any individual piece of equipment is available to operate 16 hours/day, but 2 hours (in total) are lost each day on each piece of equipment due to breaks and meetings when operators are not available to operate the equipment. how many minutes/day are available for production