Question

In the game of​ roulette, a wheel consists of 54 slots numbered​ 00, 0,​ 1, 2,..., 54. To play the​ game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Complete parts​ (a) through​ (c).

a) What is the sample space?
b) Determine the probability the metal ball falls into the slot marked 7.
c) What is the probability the ball lands in an “odd” slot?
d) Interpret this probability: 27/56 = 0.4821 …

Answer 1

Explanation:

Consider the provided information.

A wheel consists of 54 slots numbered​ 00, 0,​ 1, 2,..., 54

Part A:

The sample space is the slots on which the ball can fall.

Here wheel consists of 54 slots numbered. Thus the sample. So, there are total 56 slots and the sample space is {00, 0,​ 1, 2,..., 54}

Part B:

There are 56 slots and only one slot marked by 7. There is an equivalent likelihood that it will fall into any of these slots.

Thus, the probability of the metal ball falls into the slot marked 7 is:

P(A) = 1/56 = 0.0178

Hence, the probability of the metal ball falls into the slot marked 7 is 0.0178.

Part C:

The number of odd slots are 1, 3, 5...55.

There are total 27 odd numbers and 56 slots.

Thus, the probability of the ball lands in an “odd” slot is:

P(A) = 27/56 = 0.4821

Hence, the probability of the metal ball falls an “odd” slot is 0.4821.

Part D:

Interpret this probability: 27/56 = 0.4821 …

The probability of the ball will fall on odd slot is around 48.21% or we can say, if we spins the wheel 100 times then ball will land on odd place around 48 times.