Logs (cylindrical trunks) are made in the following way at Hód Kft. The circular saw machine first cuts off two sides, marked dark in the figure, and then, after turning the wood 90 °, produces a square beam with a similar cut.

The machine is set so that the resulting base plate is as large as possible. Now a circular cylindrical 60 cm diameter 5 meter log is sawn.

a) Is it true that the volume of the resulting square beam is less than 1 cubic meter?

Hód Ltd. also manufactures timber, for which we buy wood from the producer at a purchase price of 30 000 HUF / m3. During production, the purchased wood is approx. 40% of it will become waste wood. The company sells 1 cubic meter of the finished product for 90 000 HUF, but it has to spend 35% of the selling price on costs (processing, site maintenance, etc.)

b) How much profit does Hód Kft. generate on selling 1 cubic meter of timber?

Six trucks leave the logging company site in succession. Four trucks deliver pine and two deliver oak.

c) Calculate the probability that the two trucks transporting the oak will leave the site in succession if the cars have a random start order.