Can someone show me how to find the probability algebraically?
Two dice are rolled. Find the probability of each event. a. the sum of the number is 10. b. the sum is at least 10. c. at least one die shows a 4. d. exactly one die shows a 4.

Question

Can someone show me how to find the probability algebraically?
Two dice are rolled. Find the probability of each event. a. the sum of the number is 10. b. the sum is at least 10. c. at least one die shows a 4. d. exactly one die shows a 4.

jim_thompson5910 · Answer

Use a dice chart like this

jim_thompson5910 · Answer

focus on the numbers in black

how many numbers are 10?

algtrigcalc · Answer

3 numbers

jim_thompson5910 · Answer

out of how many black numbers total?

algtrigcalc · Answer

3/36 = 1/12

jim_thompson5910 · Answer

very good, that's the final answer to part A

algtrigcalc · Answer

Is there a way to do it algebraically? In case my teacher gives me larger numbers?

jim_thompson5910 · Answer

well there are 6 ways to roll 1 die, so there are 6*6 = 36 ways to roll both dice

jim_thompson5910 · Answer

there are 3 ways to add to 10

4+6 = 10
5+5 = 10
6+4 = 10

jim_thompson5910 · Answer

There isn't an algebraic way in terms of having a formula or solving for x or anything like that.

algtrigcalc · Answer

Oh ok

algtrigcalc · Answer

I understand the rest. Thank you!

jim_thompson5910 · Answer

I'm glad I could help