A jar contains 45 red candies and 60 black candies. Suppose a candy is selected at random. What are the odds against selecting a red candy?
3 to 7
4 to 3
4 to 7
can someone show me how to find the correct answer (Not the answer) but the steps ?!!!
the "odds" of some event is very closely tied in with finding probabilities.
in this case you want the
odds against some event.
so find the probability in favour of the event
then the probability against that event
The odds against the event = (the probability against that event ) : (the probability in favour of the event)
once you do your arithmetic you will realize that the denominators with cancel
e.g. the prob of some event = 4/7
then the prob against that event = 1 - 4/7 = 3/7
the odds in favour of the event = 4/7 : 3/7 = 4 : 3
note that the odds against the event = 3/7 : 4/7 = 3 : 4
To find the odds against selecting a red candy, we need to determine the number of favorable outcomes (selecting a non-red candy) and the number of unfavorable outcomes (selecting a red candy).
Step 1: Determine the total number of candies in the jar.
- 45 red candies + 60 black candies = 105 total candies
Step 2: Calculate the number of favorable outcomes (selecting a non-red candy).
- We know that there are 60 black candies in the jar.
Step 3: Calculate the number of unfavorable outcomes (selecting a red candy).
- We know that there are 45 red candies in the jar.
Step 4: Find the odds against selecting a red candy.
- The ratio of favorable outcomes to unfavorable outcomes gives us the odds.
- In this case, the odds against selecting a red candy would be 60 (favorable outcomes) to 45 (unfavorable outcomes), which simplifies to 4 to 3.
Therefore, the correct answer would be "4 to 3" as the odds against selecting a red candy.