Probability: Single die, mulitlple throws - What is the probability of getting a 1 within 2 throws?

Question

Know that getting a 1 in any single throws is 1/6. Getting a 1 both times in 2 throws is 1/6 x 1/6 = 1/36. However, what is the probability of getting a 1 at least once in two throws? Seems too high to just say 1/6 + 1/6 = 1/3?

Answer 1

There are different ways of getting "at least" one "1", so you have to take those possibilities into account. It should be:

P(getting a 1 on the first, but not the second) + P(getting a 1 on the second, but not the first) + P(getting a 1 on both)

This is
(1/6)(5/6) + (1/6)(5/6) + (1/6)(1/6)
5/36 + 5/36 + 1/36
11/36

Another way to calculate this is to say the probability is
1 - P(you get NO 1s on either throw) =
1 - (5/6)(5/6) =
1 - 25/36 =
11/36

Answer 2

there are 36 possibilities total if a single dice is throw twice.

you can find the probability of at least getting a 1 by find the probability of geting no 1 and subtract from 1

1 - 5/6*5/6 = 11/36

or you can count it.

1 and N
N and 1
1 and 1

the first 1 can go with any of the remaining 5. So there are 5 ways

the second 1 can go with any of the remaining 5. So there are also 5 ways

1 and 1 is another way

so p = (1 + 5 + 5) / 36 = 11/36

Answer 3

assuming a fair die

Probability of getting a 1 on the first throw: 1/6
Probability of not a 1 on first throw and a 1 on the second = 5/6*1/6 = 5/36
Probability of getting a one on both throws: 1/6*1/6 = 1/36

sum all probabilities together and 1/6 + 5/36 + 1/36 = 12/36 = 1/3

Q.E.D

Answer 4

I think the easiest way to see this is as follows:

You can get a 1 on the first throw.

*OR*

you get a non-1 on the first throw and a 1 on the second throw.

Note this discription makes the sets disjoint. The probabiliites are

1/6 + 5/6 * 1/6 = 11/36

Answer 5

yep - 1/3 - the same (in terms of long-term probability) as thowing 2 dice at once and needing only one of them to come up a 1... however, as in all real appication sof probability, in independant tests, the probability of throwing a 1 on EACH throw is always 1/6 - over time, you'll see the 1/3 emerge for consecutive throws. But everytime you roll a die, your chance of a one ON THAT THROW remains 1/6.

Not an expert though... curious to see if any math whizzes disagree...

Answer 6

1- (5/6 *1/6 + 5/6* 1/6 + 1/6*1/6).