1/6 x 1/6 = 1/36
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The odds of rolling snake eyes (two ones) on a pair of dice is 1 in 36, since there are 36 possible outcomes when rolling two dice. To find the odds of rolling snake eyes twice in a row, you multiply the probabilities: ( \frac{1}{36} \times \frac{1}{36} = \frac{1}{1296} ). Therefore, the odds of rolling snake eyes twice in a row are 1 in 1296.
Odds of rolling seven once (2 dice) is 1:6, twice in a row, odds are 1:36. The reason is- the first die can be any number, but the second die must be a particular number. For example, if the first die is 6, then the second die has to be 1 to make 7. When an event occurs twice, and the two events are unrelated, then you can multiply the odds together= 1/6 * 1/6 = 1/36.
The odds of sinking the 8 ball on the break in a standard game of pool are typically around 1 in 40. To calculate the odds of sinking it twice in a row, you would multiply the probability of sinking it once (1/40) by itself, resulting in a probability of approximately 1 in 1,600. This means that the chances of sinking the 8 ball on the break twice in a row are quite low.
Each element of a row of pascal's triangle is the sum of the two elements above it. Therefore when you some the elements of a row, each of the elements of the row above are being summed twice. Thus the sum of each row of pascal's triangle is twice the sum of the previous row.