A typical roulette wheel used in a casino has 38 slots that are numbered 1, 2, 3, ... , 36, 0, 00, respectively The 0 and 00 slots are colored green. Half of the remain ing slots are red and half are black. Also, half of the integers between 1 and 36 inclusive are odd, half are even, and 0 and 00 are defined to be neither odd nor even. A ball is rolled around the wheel and ends up in one of the slots; we assume that each slot has equal probability of 1/38, and we are interested in the number of the slot into which the ball falls.
a. Define the sample space S.
b. Let A = {0, 00}. Give the value of P(A).
c. Let B = {14, 15, 17, 18}. Give the value of P(B).
d. Let D = {x : x is odd}. Give the value of P(D).

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codiepienagoya codiepienagoya · Answer 1 · 2021-02-23T04:45:47+01:00

Answer:

Follows are the solution to the given points:

Step-by-step explanation:

For point a:

Space for results All possible outcomes are:

[tex]\to O = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,}[/tex]

[tex]17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, \\ 29, 30, 31, 32, 33, 34, 35, 36, 0, 00}[/tex]

For point b:

[tex]\to P(A) = \frac{ \text{ \# of outcomes in A}}{ \text{ \# Total outcomes}} = \frac{2}{38} = 0.052[/tex]

For point c:

[tex]\to P(B) = \frac{ \text{ \# of outcomes in B}}{\text{ \# Total outcomes}} = \frac{4}{38} = 0.105[/tex]

For point d:

We consider that in D there are 18 elements (only Odd numbers in the range 1 to 36)

[tex]\to P(D) = \frac{ \text{\# of outcomes in D}}{\text{\# Total outcomes}} = \frac{18}{38} = 0.473[/tex]