Question

In the popular American game of roulette, the roulette wheel has 38 spaces that are numbered 0, 00, and 1 through 36, 0.
Find the probability of getting the following:

a) A number that is less than 15, not counting 0 and 00;
b) A number that is a multiple of 3 or 5, not counting 0 and 00;
c) An odd number that is less than 15, not counting 0 and 00;
d) A number that is between 1 and 12, inclusive.

Answer 1

Solution:

total number of spaces = 38

( a )

number of spaces less than 15 = 14 ( excluding 15 )

probability of getting a number less than 15 = 14 /38 = 0.3684

( b )

multiples of 3 are

3,6,9,12,15,18,21,24,27,30,33,36

number of multiples are three = 12

multiples of 5 are

5,10,15,20,25,30,35

number of 5 multiples = 7

total number of multiples of 3 and 5 = 12 + 7 - 5( since 15 and 30 are common multiples )

= 17

probability of getting a number of that is multiple of 3 or 5 = 17 / 38 = 0.4473

( c )

odd numbers less than 15 are

1,3,5,7,9,11,13

number of odd numbers less than 15 = 7

probability of getting a odd number less than 15 = 7 / 38 = 0.1842

( d )

numbers that are between 1 and 12 inclusive = 12

probability of getting a number between 1 and 12 inclusive = 12 / 38 = 0.3157