Math Help - Probability questions (shouldnt take long)

1. Probability questions (shouldnt take long)

I generally know how the problems work, but while doing work I got stuck on these two. How do you set them up?

1) A coin is flipped three times and a die is rolled. Find the probability of tails showing twice and the die showing six

Now since its using "and", i'm pretty sure it wants me to multiply.

would this be right? (1/2 + 2/3)x(1/6)

2) Two dice are rolled. Find the probability that at least one die shows 3 or both dice show the same number.

it uses "or" so it wants to add..

so (1/6)+(1/6)+(2/12) - 2/12 ?
(with the 1/6's being the chance for 3 and the +2/12 the chance for same number and -2/12 being the chance for both)

If you can help, i'd very much appreciate it! thank you

2. Does these answers seem reasonable to anyone?
I looked more and i think the first one is right but not quite sure on the second still

3. Originally Posted by 3deltat
1) A coin is flipped three times and a die is rolled. Find the probability of tails showing twice and the die showing six

Now since its using "and", i'm pretty sure it wants me to multiply.

would this be right? (1/2 + 2/3)x(1/6)
ok, i'm a bit rusty on probability, too rusty, in fact, to help you with the second one. but i believe both your answers are wrong. here's how i think the first one should go:

the coin is flipped 3 times, so there are three ways for tails to show exactly 2 times

first way: tails on first flip, tails on second flip, no tails on third flip
second way: tails on first flip, no tails on second flip, tails on third flip
third way: no tails on first flip, tails on second flip, tails on third flip

probabilities:

first way: (1/2)(1/2)(1/2) = 1/8
second way: (1/2)(1/2)(1/2) = 1/8
third way: (1/2)(1/2)(1/2) = 1/8

so to get exactly 2 tails we can get them the first way OR the second way OR the third way

probability: 1/8 + 1/8 + 1/8 = 3/8

now the probability that the die shows 6 is 1/6

so the probability that we get 2 tails AND the die showing 6 is:

3/8 * 1/6 = 1/16

4. Originally Posted by 3deltat
2) Two dice are rolled. Find the probability that at least one die shows 3 or both dice show the same number.
i believe the shortest most elegant way to do this problem uses a formula in probability that utilizes binomial expansion--have you seen such a method in your class?

the other way is a lot of calculations i can tell you that much--but i don't remember how to do it. i think i got the first part down("the probability that at least one die shows 3"), but i don't recall how to combine that with the second part