Some STEP probability and mechanics questions from Michael Gibson’s “mini-mock” papers. These questions can be done with relatively short working and without needing to use any great knowledge of formulas. Continue reading
Worked solutions to:
Question: I choose at random an integer in the range 10000 to 99999, all choices being equally likely. Given that my choice does not contain the digits 0, 6, 7, 8 or 9, show that the expected number of different digits in my choice is 3.3616. Continue reading
A prison consists of a square courtyard of side b bounded by a perimeter wall and a square building of side a placed centrally within the courtyard. The sides of the building are parallel to the perimeter walls.
Guards can stand either at the middle of a perimeter wall or in a corner of the courtyard.
If the guards wish to see as great a length of the perimeter wall as possible, determine which of these positions is preferable.
You should consider separately the cases b < 3a and b > 3a.