Kyle challenges you to a game. Each player rolls a standard number cube twice. If the sum of the results is divisible by 3, you
win. If it is not, Kyle wins. What is your probability of winning? Is this a fair game?
1 answer:
Answer:
The probability of you winning is 1/3
No, it is not a fair game
Step-by-step explanation:
The first thing we need to have here is the sample space. This refers to the set of all possible results that can occur from the rolling.
Please check attachment for this
Kindly note that the total number of possible outcomes is 36.
And in the attachment, sums which are divisible by 3 are circled.
The number of circles we can count is 12
Thus, the probability of you winning would be number of circles/total number of outcomes = 12/36 = 1/3
Is it a fair game?
No, it is not
It can only be a fair game if the probability of winning equals probability of losing ( which is 18/36 = 1/2 or 0.5)
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Explanation:
To achive that you have to piant a ring in red, which will have its big diameter equal to the sphere diameter and its small diameter equal to the cube diagonal.
The diagonal of the cube can be calculated using Pithagoras:
Where D is the diagonal and L is the side of the cube