An ordinary dice is rolled what are the odds against and in favour of the event "multiple of Three"?
To determine the odds against and in favor of an event, we first need to understand the probability of that event occurring.
In this case, we are interested in finding the probability of rolling a multiple of three on an ordinary six-sided dice. To do this, we need to identify the favorable outcomes (the numbers that are multiples of three) and the total number of possible outcomes.
The favorable outcomes are 3 and 6, since they are the two numbers that are multiples of three on a typical six-sided dice.
The total number of possible outcomes is 6, as there are six sides on the dice, numbered 1 through 6.
So, the probability of rolling a multiple of three is 2/6, which simplifies to 1/3.
Now, to determine the odds against and in favor of this event, we use the formula:
Odds against = (1 - Probability) / Probability
Odds in favor = Probability / (1 - Probability)
Let's calculate:
Odds against = (1 - 1/3) / (1/3)
= (2/3) / (1/3)
= 2/1
= 2:1
Odds in favor = (1/3) / (1 - 1/3)
= (1/3) / (2/3)
= 1/2
= 1:2
Therefore, the odds against rolling a multiple of three are 2:1, and the odds in favor are 1:2.
multiple of three:3 or 6
pr (3or6)=2/6=1/3
pr(not 3or6)=1-1/3=2/3
so the odds against multiple of three = (2/3) : (1/3)
= 2 : 1
the odds in favour of multiples of three = 1 : 2