The Floor is Lava!

With a $D20$ , you have a $\frac{14}{20}$ chance of rolling a 7 or higher. So, the probability of success is $\fbox{.70}$ on $2D10$ .

Rolling the 2 $D10$ , there are 10 possible rolls with the first die, each of which is equally likely, and then 10 possible rolls for the second die. So there are $10^2 = 100$ possible events total, each of which is equally likely, and we must figure out how many of them are successes.

Given each possible roll on die one, how many ways could die 2 come up that would mean success (a total of 7 or greater on both dice)?

roll a 0 on die 1 ==> you must roll a 7, 8, or 9 on die 2 ----- 3 ways
roll a 1 on die 1 ==> you must roll a 6, 7, 8, or 9 on die 2 ----- 4 ways
roll a 2 on die 1 ==> you must roll a 5, 6, 7, 8, or 9 on die 2 ----- 5 ways
roll a 3 on die 1 ==> you must roll a 4, 5, 6, 7, 8, or 9 on die 2 ----- 6 ways
roll a 4 on die 1 ==> you must roll anything but a 0, 1, or 2 on die 2 ----- 7 ways
roll a 5 on die 1 ==> you must roll anything but a 0 or 1 on die 2 ----- 8 ways
roll a 6 on die 1 ==> you must roll anything but a 0 on die 2 ----- 9 ways
roll a 7 on die 1 ==> you can roll anything on die 2 on die 2 ----- 10 ways
roll a 8 on die 1 ==> you can roll anything on die 2 on die 2 ----- 10 ways
roll a 9 on die 1 ==> you can roll anything on die 2 on die 2 ----- 10 ways

So 72 ways total. So there are 72 events that are successful out of 100 possible events. Therefore the probability of succeeding is $\fbox{.72}$ on $2D10$ .

Faster and easier looking only at the probability of losing! With the 20 sided, that would be 6 out of 20. 30 %. With the two 10 sided, there are 100 possible combinations, of which 28 lose. (one way to roll zero, two ways to roll 1, three ways to roll 2, four ways to roll 3, five ways to roll 4, six to roll 5, and seven to roll 6. That adds up to 28 losing possibilities. ) 28 % chance to lose. Better odds than 30 %.

Roll the pair of 10 sided dices.

• With the pair of 10 sided dice, 72 combinations out of 100 add up 7 or higher (odds are 72%)

• With the 20 sided dice, 14 out of 20 faces are 7 or higher (odds are 70%)

The blue dice pictured are actually 8-sided dice :)

There are 55 different combinations of the numbers 0 to 9 on the 2 dice. 39 of them have sums of 7 or greater. 39/55 = 70.9090909% The 20-sided die has 14 numbers greater than or equal to 7. 14/20 = 70%

For a 20-sided die with sides numbered 1 to 20 , the probability to come up with a number greater than or equal to 7 = $\frac{14}{20}$ = 0.7 .

However. for a 10-sided die with sides numbered 0 to 9 , the probability to come up with a number greater than or equal to 7 will be sum of the all kinds of combinations like so,

Assuming the first die gets a 9, then any one of the 10 numbers on the second die would fetch a sum greater than or equal to 7 . Probability for the aforementioned case = $\frac{1}{10}$ * $\frac{10}{10}$ = $\frac{10}{100}$ .

Similarly if we were to sum the probabilities for all the numbers from 9 to 0, we would end up with an expression like so, $\frac{10}{100}$ + $\frac{10}{100}$ + $\frac{10}{100}$ + $\frac{9}{100}$ + $\frac{8}{100}$ + $\frac{7}{100}$ + $\frac{6}{100}$ + $\frac{5}{100}$ + $\frac{4}{100}$ + $\frac{3}{100}$ = $\frac{72}{100}$ = 0.72 .

|I know that with two d6 dice, 7 is the most likely outcome, because there are more combinations that add up to 7 than any other number. On that basis, I went for the two d10

The two 10 sided dice give you a better chance of rolling a 7 or better There are 28 ways out of 100 - or 28% - chance not to roll a 7 with two 10 sided dice.

First die 0 second die 0-6 seven ways

First die 1 second die 0-5 six ways

First die 2 second die 0-4 five ways

First die 3 second die 0-3 four ways

First die 4 second die 0-2 three ways

First die 5 second die 0-1 two ways

First die 6 second die 0 one way

                                         = 28/100

So if you wouldn't roll a 7 28% of the time that means you will roll a 7 or better 72% of the time

With the one 20 sided die you have a 14/20 - or 70% - chance of rolling a 7 or better