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# System prepended metadata

title: 'Lab 26: Probability Practice'

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# Lab 26: Probability Practice

## Problem: Roleplaying

**a**. 

$\Omega = \{1,...,20\}$

$E = \{(15),(16),(17),(18),(19),(20)\}$

$p(E) = \frac{3}{10}$

**b**. 

$\Omega = \{1,...,20\}$

For Failures then subtract this from 1

$E_1 = \{(1),..., (14)\}$

$E_2 = \{(1),..., (14)\}$

$p(E_1) = 7/10 = p(E_2)$

$p(E_1 \cap E_2) = p(E_1) \times p(E_2)$

$1-.49 = .51 = p(E_1 \cap E_2)$

**c**. 

$\Omega = \{1,...,20\}$

$E_1 = \{(15),(16),(17),(18),(19),(20)\}$

$E_2 = \{(15),(16),(17),(18),(19),(20)\}$

$p(E_1) = 3/10 = p(E_2)$

$p(E_1 \cap E_2) = p(E_1) \times p(E_2)$

$p(E_1 \cap E_2) = 3/10*3/10 = 0.09$

**d**. 

$\Omega = \{1,...,20\}$


$E = \{(8 + i + s - d), ..., (20)\}$

$p(E) = \frac{20 - (8 + i + s - d) - 1}{20}$

$p(E) = \frac{11 - i - s + d}{20}$

**e**.

Probability of not resisting disintegration: $1 - \frac{11 - i - s + d}{20}$

If $10d6+40 >= h$ than they lose

i = 2, s = 4, d = 1, h = 90.

14/20 chance that the spell is not resisted. Within that 14/20 chance, what is the chance 10d6 is greater than 90.

$\Omega = \{10,...,60\}$

$E = \{(50), ..., (60)\}$ it disinigrates victim in these cases

$P(E) = 1/5$

Probability of victim being disintigrated in this conrete example = 1/5 * 14/20 = 14 / 100 or 14%. 









