Given the following probabilities for an event E, find the odds for and against E. (A) eight ninths (B) seven ninths (C) 0.59 (D) 0.71

(a) The odds for and against E are (8:1) and (1:8) respectively.

(b) The odds for and against E are (7:2) and (2:7) respectively.

(c) The odds for and against E are (59:41) and (41:59) respectively.

(d) The odds for and against E are (71:29) and (29:71) respectively.

Step-by-step explanation:

The formula for the odds for an events E and against and event E are:

(a)

The probability of the event E is:

Compute the odds for and against E as follows:

Thus, the odds for and against E are (8:1) and (1:8) respectively.

(b)

The probability of the event E is:

Compute the odds for and against E as follows:

Thus, the odds for and against E are (7:2) and (2:7) respectively.

(c)

The probability of the event E is:

Compute the odds for and against E as follows:

Thus, the odds for and against E are (59:41) and (41:59) respectively.

(d)

The probability of the event E is:

Compute the odds for and against E as follows:

Thus, the odds for and against E are (71:29) and (29:71) respectively.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

hit or miss i guess they never miss huh

step-by-step explanation:

you got a boyfriend i bet he doesnt kiss ya