Maths Quiz - New Tasks
This time we will deal with stochastics.
Level "Easy":
A sniper is seeing three tins marked with A, B, C in front of him. When he shoots, the chance that he hits any tin is 60%; the chance that he hits a particular tin, however, is only 20%. What's the chance that, after shooting three times, he has hit tins A, B, C in exactly this order? What's the chance that, after shooting three times, he has hit no tin at all? And how much is the latter possibility more likely than the first?
Level "Medium":
What's the chance that two particular persons were born on the same day? Note that this is not about a particular day, but about any day in the year. You must assume that a year consists of 366 days.
Level "Hard":
A mad coder has written a perfect random numbers generator which works with the data-type unsigned char (i.e. it returns numbers in the range of 0 to 255). The special feature of the function is that every time you call it, the output value is at least as large as the previous one. The coder runs his function 10 times and adds the returned values to a long int variable in order to prevent overflow errors. How many possibilities are there to get a total sum of 1815?
Enjoy exerting your brains!