The probability that mary will win a game is 0.02, so the probability that she will not win is 0.98. if mary wins, she will be given $160; if she loses, she must pay $16. if x = amount of money mary wins (or loses), what is the expected value of x? (round your answer to the nearest cent.)

Given:

Probability of winning, P(X) = 0.02

Probability of losing, P() = 0.98

Wining amount = $160

Losing amount = $16

Step-by-step explanation:

Let the expected amount of money win be  'X'

Expected value of X, E(X) = Probability of winning, P(X).Probability of winning, P(X)  - Probability of losing, P().Losing amount

Now,

E(X) = ()

E(X) = -12.48

Expected value of X = -12.48

Expected loss value = $12.48 loss

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.