Question

What is the probability of rolling two six sided dice and obtaining the following?

a) 2 and 3
b) 6 and 6
c) at least one 6
d) two of the same number
e) even number of both dice
an even number on at least one dice

Answer 1

can someone plese explain. im not understanding a and b

Answer 2

it is not real clear

Answer 3

if it means a two and a six as in one die is a two, the other is a six, then there are 2 ways to do that and 36 total outcomes so \(\frac{2}{36}\) or if you prefer \(\frac{1}{18}\)

Answer 4

only one way to get double 6, so \(\frac{1}{36}\)

Answer 5

could u please explain why there are 36 outcomes? my teacher wants me to explain how to do this problem with the addition and multiplication rule but im not sure how to apply that here

Answer 6

There are 36 outcomes because a regular dice has 6 possible outcomes. So two dice, 6*6 = 36.

For question a)
P(A and B) = P(A) * P(B)
In human english, this means probability of A and B is equal to Prob of A * Prob of B

So for A,
P(Rolling a 2 and a 3) = P(rolling a 2 on the first die) * P(rolling a 3 on the second die)

NOTE that the probability of rolling ANY number on a die is 1/6, this makes sense obviously.

So:
P(rolling a 2 and a 3) = (1/6) * (1/6) = 1/36

Basically, in probability, the word "AND" means to multiply. The word "OR" means to add.

So for b) It's the same answer, 1/36.

c) At least one 6. This can be translated to "At least NO 6's". Which is simply:
1 - probability of no sixes on each die
Probability of not getting a 6 on a die... logic tells me this is 5/6... duh
1 - (5/6)(5/6)
11/36

The rest of the questions are basically using logic like this. I hope this helps.

Answer 7

hi IsTim, thanks for your help, i still don't understand a. b/c the answer is 1/18 but i also got 1/36 like you. do u happen to know why its 1/18?

Answer 8

Ah, my mistake, I see. It is 2/36, which is actually 1/18. Visualize all the probabilities into tuples:


(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)


Rolling a 2 and a 3, doesn't mean 2 on the first die, and 3 on the second, it means 2 and 3 OR 3 and 2.

Notice there are two possible outcomes out of 36 which satisfy this claim.
(2,3), (3,2)

I.e
probability is 1/18

Answer 9

For B however, the answer is 1/36.

Answer 10

ohh that makes so much more sense now! thanks IsTim. you've saved the day! :)