The faces of a green tetrahedron die are marked 10,20,30 and 40. All three die are thrown together and the scores added. Find the probability that the total is more than 30 but less than 35.
Assuming all three die are identical...
ways to get 30
40, any two others
30, and any two others
20, and any two others
10, and any two others, one of which is greater than 10.
So the probablity of getting greater than 30 is
Pr(>30)=1-pr(three 10s)=1-1/4 ^3
ways of getting less than 35
three 10's
Well, that sort of messes things up for getting over 30..
so Pr ( 30<total<35)=0
To find the probability that the total score is more than 30 but less than 35 when three dice are thrown, we need to determine the number of favorable outcomes and the number of possible outcomes.
First, let's find the number of possible outcomes. Each die has 4 faces, so each die can land on one of the 4 numbers. Since there are 3 dice being thrown simultaneously, the total number of possible outcomes is 4^3 = 64.
Next, let's determine the number of favorable outcomes. The only way to get a total score between 30 and 35 is if the highest number rolled is a 10 and the other two dice land on numbers that sum up to a value between 20 and 25. We can break this down into cases:
Case 1: The highest number rolled is 10:
In this case, the remaining two dice need to land on numbers that sum up to a value between 20 and 25. The possible outcomes for the other two dice are:
(20,20), (20,30), (30,20), (10,30), (30,10)
Case 2: The highest number rolled is 20:
In this case, one of the other two dice must land on 10, while the remaining die can be any of the remaining three numbers. The possible outcomes for the other two dice are:
(10,10), (10,30), (10,40), (20,10), (20,30), (20,40)
Note: We don't consider the case where the highest number rolled is 30 or 40, as the total score would be greater than 35.
So, there are a total of 5 + 6 = 11 favorable outcomes.
Therefore, the probability of getting a total score between 30 and 35 is 11 (favorable outcomes) / 64 (possible outcomes).
So, the probability is 11/64, or approximately 0.172.
In conclusion, the probability that the total score is more than 30 but less than 35 is approximately 0.172.