2 years ago

What is the theoretical probability of rolling all 5 dice on the same number?

1 answer:

4 0

The theoretical probability of (for example) rolling 5 ones is 1/(6^5) or approximately 0.013%. Because it doesn't matter which number we get five of we can multiply it by 6 to get 1/(6^5) or approximately 0.077%.

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Show that if f(n) is O(g(n)) and d(n) is O(h(n)) then f(n) + d(n) is O(g(n) + h(n)).

GaryK [48]

$f(n)\in\mathcal O(g(n))$ is to say

$|f(n)|\le M_1|g(n)|$

for all $n$ beyond some fixed $n_1$ .

Similarly, $d(n)\in\mathcal O(h(n))$ is to say

$|d(n)|\le M_2|h(n)|$

for all $n\ge n_2$ .

From this we can gather that

$|f(n)+d(n)|\le|f(n)|+|d(n)|\le M_1|g(n)|+M_2|h(n)|\le M(|g(n)|+|h(n)|)$

where $M$ is the larger of the two values $M_1$ and $M_2$ , or $M=\max\{M_1,M_2\}$ . Then the last term is bounded above by

$M(|g(n)|+|h(n)|)\le2M\max\{|g(n)|,|h(n)|\}$

from which it follows that

$f(n)+d(n)\in\mathcal O(\max\{g(n),h(n)\})$

3 0

2 years ago

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Butoxors [25]

A angle 2
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2 years ago

Simplify the expression <br> -7(3e-2f+4)+6e-2

Shkiper50 [21]

Answer: here it is 14f-30-15e

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3 years ago