Probability Two tetrahedral dice are thrown

In summary, when two tetrahedral dice are thrown, the probability of getting an even or prime sum is 9/16. This can be found by first listing out all possible outcomes and then finding the number of outcomes that have an even or prime sum. Another method is to find the number of odd, non-prime sums and subtracting it from the total number of outcomes (16).
  • #1
thornluke
37
0

Homework Statement


Two tetrahedral dice (four-sided dice) are thrown. What is the probability that the sum of the scores is:
a) even
b) prime
c) even or prime?

Homework Equations





The Attempt at a Solution


a) P(even) = 1/2
b) P(prime) = 9/16

c) c for confused :confused:

Can someone please explain the theory behind answering Question c?

Cheers.
 
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  • #2
Have you written out the set of "outcomes"? A tetrahedron has four sides so it has the numbers 1, 2, 3, and 4. The possible outcomes when two are thrown are (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), and (4, 4). There are, of course, [itex]4^2= 16[/itex] outcomes and each is equally likely. How many have sums that are either even or prime?
 
  • #3
HallsofIvy said:
Have you written out the set of "outcomes"? A tetrahedron has four sides so it has the numbers 1, 2, 3, and 4. The possible outcomes when two are thrown are (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), and (4, 4). There are, of course, [itex]4^2= 16[/itex] outcomes and each is equally likely. How many have sums that are either even or prime?

Ah... 2 is a prime number too.. I see now.
My mind has gone mad from all these probability questions..
 
  • #4
It wasn't until now that I worked out the answer to (c) myself and I was very surprised at the answer!
 
  • #5
HallsofIvy said:
It wasn't until now that I worked out the answer to (c) myself and I was very surprised at the answer!
There is an easy way to find this probability:
How many odd, non-prime numbers are possible as sum?
All numbers which are not [odd and not prime] are even or prime.
 

FAQ: Probability Two tetrahedral dice are thrown

What is the probability of rolling a specific number on both dice?

The probability of rolling a specific number on both dice is 1/16, or 6.25%. This is because there are 16 possible outcomes when rolling two tetrahedral dice (4 possible outcomes for each die), and only one of those outcomes will result in both dice showing the specific number.

What is the probability of rolling a higher number on the second die than the first?

The probability of rolling a higher number on the second die than the first is 5/12, or 41.67%. This is because there are 12 possible outcomes where the second die is higher than the first (such as rolling a 2 on the first die and a 3, 4, or 5 on the second die), out of the total 16 possible outcomes.

What is the probability of rolling a total of 7 on the two dice?

The probability of rolling a total of 7 on the two dice is 1/6, or 16.67%. This is because there are 6 possible ways to roll a total of 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of the total 36 possible outcomes (4 possible outcomes for each die, so 4x4=16, and 16x2=36).

What is the probability of rolling at least one even number?

The probability of rolling at least one even number is 3/4, or 75%. This is because there are 4 possible outcomes for each die (1, 2, 3, or 4), and only one of those outcomes will result in an odd number (1 or 3). Therefore, the probability of rolling at least one even number is 1 - (1/4 x 1/4) = 3/4.

What is the probability of rolling two of the same number on both dice?

The probability of rolling two of the same number on both dice is 1/4, or 25%. This is because there are 4 possible outcomes for each die (1, 2, 3, or 4), and only one of those outcomes will result in both dice showing the same number (2+2, 3+3, or 4+4). Therefore, the probability of rolling two of the same number on both dice is 1/4 x 1/4 = 1/16, or 25%.

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