5. In a party game, a bottle is spun and whoever it points to when it stops has to play next. The acute angle, in degrees, that the bottle makes with the side of the room is modelled by a rectangular distribution over the interval [0,90].
Find the probability that on one spin this angle is
- between \(25 ^ { \circ }\) and \(38 ^ { \circ }\),
- \(45 ^ { \circ }\) to the nearest degree.
The bottle is spun ten times.
- Find the probability that the acute angle it makes with the side of the room is less than \(10 ^ { \circ }\) more than twice.