Math novice here. With a 10-sided die, the probably of rolling '1' is 10%. I'm tempted to think the probability of rolling '1' with two consecutive rolls is 20%. Would I be correct?
Not sure if I need to factor in the first roll i.e. 10% + (10% – probability of NOT rolling 1 in the first roll). Or am I overthinking this?
CLARIFICATION:
I mean the probability of rolling a 1, then another 1.
Best Answer
Think of a $10 \times 10$ array of squares, where each square represents a possible roll. For example, we could say the square in row $a$ column $b$ corresponds to rolling an $a$ first, and then rolling a $b$.
With these $100$ different possibilities, only one of them - the one in the top left hand corner - corresponds to rolling two consecutive $1$s.
Therefore, the probability is $1/100 = 1\%$.
(More generally, you want to be multiplying the probabilities of independent events rather than adding them. This sometimes goes by the name of the "multiplication rule.")