Question

Which is more likely to occur (i.e. has a higher probability):
a. Rolling a 2 or higher on a single 6 sided die
b. Rolling a 3 or higher on a single 6 sided die, if you can re-roll the die if
you fail the first time

Answer 1

First, what's the probability of getting a 2 or higher on a 6 sided die?

Answer 2

5/6

Answer 3

Ok, so the tricky part is 3 or higher on one of two rolls. Since we don't really care about the second roll if the first one hits, we don't need to limit ourselves to only a single hit.

What this means is that we should find the probability to NOT get a 3 or higher on a die after two rolls, and subtract that from one.

What's the probability to NOT get a 3 or higher on a 6 sided die after one roll?

Answer 4

33.2%

Answer 5

or 33%
i don't know why i put a .2

Answer 6

2/6 or 1/3, right.

So, the chance to fail to get a 3 or higher on the first roll is 1/3. It's the same on the second.
\[P(AandB)=P(A)P(B)\]

So what is the probability of rolling twice and neither roll being 3 or higher?

Answer 7

so you just multiply them 1/3 times 1/3

Answer 8

Correct. That gives the chance to NOT get a 3 or higher on either roll.

Answer 9

so 1/9

Answer 10

Right. So if the chance to NOT roll a 3 or higher is 1/9, then what is the chance to roll a 3 or higher at least once?

Answer 11

8/9

Answer 12

There ya go.

So which has the higher probability of success?

Answer 13

b does

Answer 14

And you're done! :)

Answer 15

awesome thank you

Answer 16

could i possibly ask you one more question