you have a set of flashcards 1-36. a card is chosen at random. find the odds in favor of and against each selection.
1. multiple of 3
2. prime #
3. mutliple of 2 or 3
4. mutliple of 2 and 3
5. only 1 digit
6. has more than 1 digit
I will do #3, the others care done the same way.
Numbers which are multiples of 2 or 3 ?
(easier to exclude: 1,5,7,11,13,17,19,23,25,29,31,35
there are 12 of those, so the number that are multiples of 2 or 3 are 36-12 or 24
so the prob(multiple of 2 or 3) = 24/36 = 2/3
prob(NOT a multiple of 2 or 3 ) = 1/3
Odds in favour of multiple of 2 or 3
= (2/3) : (1/3)
= 2 : 1
odds against a multiple of 2 or 3
= 1 : 2
To find the odds in favor and against each selection, we first need to determine the total number of possible outcomes and the number of favorable outcomes for each selection.
1. Multiple of 3:
There are a total of 36 possible outcomes. Out of these, there are 12 multiples of 3 (3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36). Therefore, the odds in favor of selecting a multiple of 3 are 12:36 or simplified as 1:3. The odds against selecting a multiple of 3 are 24:36 or simplified as 2:3.
2. Prime Number:
There are a total of 36 possible outcomes. Out of these, there are 11 prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31). Therefore, the odds in favor of selecting a prime number are 11:36. The odds against selecting a prime number are 25:36.
3. Multiple of 2 or 3:
There are a total of 36 possible outcomes. Out of these, there are 18 numbers that are multiples of 2 or 3 (2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 26, 27, 30, 32, 33, 36). Therefore, the odds in favor of selecting a number that is a multiple of 2 or 3 are 18:36 or simplified as 1:2. The odds against selecting a number that is a multiple of 2 or 3 are also 18:36 or simplified as 1:2.
4. Multiple of 2 and 3:
There are a total of 36 possible outcomes. Out of these, there are 6 numbers that are multiples of both 2 and 3 (6, 12, 18, 24, 30, 36). Therefore, the odds in favor of selecting a number that is a multiple of 2 and 3 are 6:36 or simplified as 1:6. The odds against selecting a number that is a multiple of 2 and 3 are 30:36 or simplified as 5:6.
5. Only 1 digit:
There are a total of 36 possible outcomes. Out of these, there are 9 numbers that have only 1 digit (1, 2, 3, 4, 5, 6, 7, 8, 9). Therefore, the odds in favor of selecting a number with only 1 digit are 9:36 or simplified as 1:4. The odds against selecting a number with only 1 digit are 27:36 or simplified as 3:4.
6. Has more than 1 digit:
There are a total of 36 possible outcomes. Out of these, there are 27 numbers that have more than 1 digit (10, 11, 12, ..., 36). Therefore, the odds in favor of selecting a number with more than 1 digit are 27:36 or simplified as 3:4. The odds against selecting a number with more than 1 digit are 9:36 or simplified as 1:4.
Note: When simplifying the odds, you can divide both the numerator and denominator by their greatest common factor to get the simplest form.