The probability that Paul wins in a raffle is given by the expression p.

Write down an expression for the probability that Paul does not win.

Step-by-step explanation:

Consider the where is sigma algebra and is probabilistic measure. Denote where Paul wins. By additivity of measure we know that

.

So

.

But is exactly the set where Paul does not win. Q.E.D.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b