BRAINLIESTTT ASAP!! PLEASE HELP ME :)

Work Shown:

event A = getting an integer between 1 and 8

event A = getting 3 points awarded

event B = getting an integer between 9 and 15

event B = getting 2 points awarded

event C = getting an integer between 16 and 19

event C = getting 1 point awarded

event D = getting the integer 20

event D = getting 0 points awarded

P(x) = probability of event x

V(x) = net value of event x

P(A) = 8/20 = 2/5

V(A) = 3

P(B) = (15-9+1)/20 = 7/20

V(B) = 2

P(C) = (19-16+1)/20 = 4/20 = 1/5

V(C) = 1

P(D) = 1/20

V(D) = 0

P(A)*V(A) = (2/5)*3 = 6/5 = 1.2

P(B)*V(B) = (7/20)*2 = 14/20 = 7/10 = 0.7

P(C)*V(C) = (1/5)*1 = 0.2

P(D)*V(D) = (1/20)*0 = 0

E[x] = expected value

E[x] = P(A)*V(A)+P(B)*V(B)+P(C)*V(C)+P(D)*V(D)

E[x] = 1.2+0.7+0.2+0

E[x] = 2.1

x = 3 ± √(5+y)