Probability, Random Variables, and Probability Distributions

The number of fire trucks is determined by a random process independent from the fire's severity.

Firefighters call in more trucks when they cause too much damage.

The severity of the fire causes more fire trucks to be present and also results in more damage.

The presence of more fire trucks leads to firefighters causing more damage.

Cannot be determined with given information.

0.60

0.50

0.50

$\frac{5}{6}$

$\frac{2}{3}$

$\frac{17}{36}$

$\frac{1}{2}$

No, because one occurring means the other cannot, which affects their occurrence

Yes, if their combined probability equals zero

Yes, but only if neither has a probability of occurring

Yes, both terms describe events that do not affect each other's outcome

Events A and B cover all possible outcome of rolling the die twice.

Events A and B are mutually exclusive.

Events A and B can both occur at the same time.

Events A and B are independent events only.

Seeing repetitive series without joint appearances still requires further testing ascertain certainty regarding nature concerning acts being Mutually Exclusive

Even after many iterations, direct comparison reveals high instances coexistence, therefore such pairs aren't truly Mutually Exclusive

Calculating total frequency over several trials shows correlation between similar picks thus negating the idea behind Mutual Exclusion

If during repeated attempts certain selections never overlap then respective chances depict their quality as Mutual Exclusions

$P(A) \times P(B) = 0.28$

$P(A \text{ and } B) > 0$

$P(A \mid B) = P(A)$

$P(A \text{ or } B) = 0.7 + 0.4$

$\frac{r \times b}{r + b}$

$r + b - (r \times b)$

$(r + b)^{n-choose-2}$

0.6

0.2

0.4

0.3

P(D) < 0.3

P(C or D) = P(C) + P(D)

P(D) > 0.7

P(D) = -0.2