Question

Find the odds for and the odds against the event rolling a fair die and getting a 2 comma a 4 comma a 5 comma or a 3.

Answer 1

The event of rolling a fair die and getting 2 or 4 or 5 or 3 has 4 possible outcomes. Either one can get 2 or 4 or 5 or 3

Number of possible ways of getting favorable outcome =4

Now remaining outcomes which are not included into event are getting 1 or 6. There are 2 outcomes.

Number of possible ways of getting unfavorable outcome =2

Odds for the event = Number of ways getting favorable outcome / Number of ways getting unfavorable outcome

Odds for given event = 4 /2 = 2/1

Odds against eventSo the odds for event of rolling a fair die and getting 2 or 4 or 5 or 3 is 2:1

Odds against event = Number of ways of getting unfavorable event / Number of ways of getting favorable event

= 2/4

=1/2

So the odds against event of rolling a fair die and getting 2 or 4 or 5 or 3 is 1:2