<h3>Answer: 2.1</h3>
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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
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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
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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
