5.1 Roulette Question:
In the game of roulette, a wheel consists of 56 slots numbered 00, 0, 1, 2, 3, … 54. To play a game, a
metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.
a) What is the sample space?
The sample space is anything the ball can land on.
{00, 0, 1, 2, 3, … 54}
b) Determine the probability the metal ball falls into the slot marked 7.
There is an equal probability of it falling into any of these slots. There are 56 total slots. There is
only ONE slot marked with a 7. Since they are all equally likely, the probability is 1/56.
1/56 = 0.017857… This is about 1.8% Which means in 100 spins it would land on the “7” about
1.8 times, so in 1,000 spins, it would land on the “7” 18 times. (because 1.8% of 1,000 is 18)
c) What is the probability the ball lands in an “odd” slot?
In the sample space {00, 0, 1, 2, 3, … 54} we have the odd numbers 1, 3, 5, 7, all the way to 53.
That is 27 total odd numbers. So out of a sample space of 56 possibilities, the probability it lands in an
odd space is 27 out of 56 or 27/56.
d) Interpret this probability: 27/56 = 0.4821 …
This is 48.21%, so in 100 spins you would land on an odd 48 times. (48% of 100 is 48)