Question

In the game of roulette, a wheel consists of 32 slots numbered 00, 0, 1, 2, . . . , 30. 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) Determine the sample space. Choose the correct answer below.
A. The sample space is {00, 0, 1, 2, . . . , 30}.
B. The sample space is {00}.
C. The sample space is {00, 0}.
D. The sample space is {1, 2, . . . , 30}.
(b) Determine the probability that the metal ball falls into the slot marked 3 and Interpret this probability by choosing the correct answer below.
A. If the wheel is spun 100 times, it is expected about 31 of those times to result in the ball landing in slot 3.
B. If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing not in slot 3.
C. If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3.
(c) Determine the probability that the metal ball lands in an odd slot and Interpret this probability by choosing the correct answer below.
A. If the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.
B. If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in an odd number.
C. If the wheel is spun 1,000 times, it

Answer 1

Answer:

(a) The sample space is {00, 0, 1, 2, . . . , 30}.

(b) If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3.

(c) If the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.

Step-by-step explanation:

We are given that in the game of roulette, a wheel consists of 32 slots numbered 00, 0, 1, 2, . . . , 30.

To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.

(a) The sample space is {00, 0, 1, 2, . . . , 30} which means the metal ball can land on any of these numbers.

(b) As we know that there is an equal probability of the metal ball landing on any of the slots marked in the sample space.

Total number of slots = 32

Number of slots marked with 3 = 1

So, the probability that the metal ball falls into the slot marked 3 is given by =  $\frac{1}{32}$  = 0.031 or 3.1%

This means that if the wheel is spun 100 times, it is expected about 3.1 of those times to result in the ball landing in slot 3.

So, if the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3 because (0.031 $\times$ 1000) = 31.

(c) As we know that the odd slot in the given sample space is {1, 3, 5,......, 29}.

Total number of slots = 32

Number of odd slots = 15

So, the probability that the metal ball lands in an odd slot is given by =  $\frac{15}{32}$  = 0.47 or 47%.

This means that if the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.