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

1 answer

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