1
3.5 Expected Value (and more probability from 3.4)
Ex a Lottery – Fantasy 5 -- Choose 5 numbers from 1 to 39
# correct
Probability
Prize value
5 of 5
$303, 811
4 of 5
$448
3 of 5
$17
2 of 5
0
1 of 5
0
Product
# of prizes
Value of
Prizes
Lottery – Mega Millions – Choose 5 numbers from 1 to 75 and one number from 1 to 15
(avoiding the VA lottery Australian rout)
Ex b In a board game, a spinner has numbers 1 – 10. Payments are as shown in the table:
Find the expected value of a single spin.
Spin
1–3
Outcome
Lose $60,000
4–6
no gain, no loss
7 – 10
Win $120,000
Find the expected value of a single spin.
2
Ex c Health Insurance Options:
Plan A - $1000/month – 100% coverage of everything allowed
Plan B - $200/month – covers nothing until $15,000 annual deductible is reached, then
covers 100% of all allowed expenses above $15,000
a) Find the annual cost of Plan A
b) A family’s annual medical expenses have the below. Find the expected value for Plan B.
Annual Expenses
Midpoint or cost paid
Probability
$0 – 5000
$2500
0.8
$5000.01 – 10,000
$7500
0.1
$10,000.01 – 15,000
$12,500
0.099
$15,000+
$15,000
0.001
c) “Plan C” is no health insurance. Suppose that the probability of a “catastrophic illness” is
0.1%, and the median catastrophic illness costs $200,000.
Plan
Premium
A
$12,000
B
$2400
C
$0
Expected out-of-pocket costs
Ex d Playing Cards (probabilities)
# of ways of drawing any 5 cards from 52 cards:
# of ways of drawing all hearts:
# of ways of drawing a flush:
# of ways of drawing 3 kings:
# of ways of drawing 3 of a
kind: