Probability Help

[Cook10]

A) What is the probability that the sum of two dice is a number less than zero?

My answer: I believe the answer is 6/36 however am not sure.

B) What is the probability that the sum of two dice is a prime number?

My answer: I believe the answer is 15/36, is that correct?

 

[pka]

A) What is the probability that the sum of two dice is a number less than zero?
My answer: I believe the answer is 6/36 however am not sure.
B) What is the probability that the sum of two dice is a prime number?
My answer: I believe the answer is 15/36, is that correct?

A) How can the sum od two dice be less than zero? Give one way!
B) List all pairs that add to \(2,3,5,7,\text{ or 11}\) Count the and divide by \(36\).

 

[Cook10]

A) How can the sum od two dice be less than zero? Give one way!
B) List all pairs that add to \(2,3,5,7,\text{ or 11}\) Count the and divide by \(36\).

For a) sorry I meant less than 5 and for b) there are 15 outcomes according to the sum of 2 dice chart so ould it be 50%

 

[pka]

A) sorry meant less than 5
B) there are 15 outcomes... so do you mean 50%

Look at this LINK
That is the generating polynomial for two dice.
The exponents are the sums and the coefficients tell us the number of ways.
Thus \(6x^7\) tells us the are six ways to toss a sum of seven. So you check it out.

 

[HallsofIvy]

The lowest two dice can add to is 2 and the highest 12:
2: 1-1 -- one way
3: 1-2 or 2-1 -- two ways
4: 3-1 or 2-2 or 1-3 -- three ways
5: 4-1 or 3-2 or 2-3 or 1-4 -- four ways
6: 5-1 or 4-2 or 3-3 or 2-4 or 1-5 -- five ways
7: 6-1 or 5-2 or 4-3 or 3-4 or 2-5 or 1- 6 -- six ways
8: 6-2 or 5-3 or 4-4 or 3-5 or 2-6 -- five ways
9: 6-3 or 5-4 or 4-5 or 3-6 -- four ways
10: 6-4 or 5-5 or 4-6 -- three ways
11: 6-5 or 5-6 -- two ways
12: 6-6 -- one way

That's a total of 1+ 2+ 3+ 4+ 5+ 6+ 5+ 4+ 3+ 2+ 1= 6x6= 36 ways.

"Less than 5" is 1, 2, 3, 4 which can happen in 0+ 1+ 2+ 3= 6 ways. The probability two dice will come up less than 5 is 6/36= 1/6.

The "prime numbers" are 2, 3, 5, 7, and 11 which can come up in 1+ 2+ 4+ 6+ 2= 15 ways. The probability two dice will come up a prime number is 15/36= 5/12.