warm-up #1
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Warm-up #1. Use the table to answer the questions. What is the probability that someone wearing their seatbelt was going >15 mph over speed limit? What is the probability that someone was going 10-15 mph OR was not wearing a seatbelt?. Expected Value. - PowerPoint PPT PresentationTRANSCRIPT
Warm-up #1Use the table to answer the questions.
1. What is the probability that someone wearing their seatbelt was going >15 mph over speed limit?
2. What is the probability that someone was going 10-15 mph OR was not wearing a seatbelt?
Number of mph over speed limit
10-15 >15 Total
Wearing Seatbelt
Yes 65 145 210
No 15 75 90
Total 80 220 300
Expected Value
• Essential Question - What is expected value used for in real-life?
What it is and what it is used for
• The expected results of an experiment in the long run.
• Used in business to predict future profits
• Used in insurance to determine how much a person’s insurance rate
• Used in games such as the lottery, slot machines, roulette to determine expected winnings (or losses)
How You Find It
• Probabilities are P
• The values of the events are x
• Expected outcome is E• E = p1x1 + p2x2 +p3x3 …..pnxn
– Multiply each probability by the amount you will win or lose then add them all together.
Interpreting Expected Value
• If you get a ZERO expected value, you expect to BREAK EVEN in the long run
• If you get a POSITIVE expected value, you expect to WIN in the long run
• If you get a NEGATIVE expected value, you expect to LOSE in the long run
• The value you get for expected value will probably NOT be one of the winnings of the game
Example 1
• If you roll a 1, I will give you $4 and if you don’t roll a 1, you give me $1.
• What is the expected value? Does this mean you will win or lose money?
• (prob of 1)($4) + (prob of NOT 1)(-$1)
• You will lose money over time
1 5($4) ( $1)
6 6
0.17
Example 2
You are taking a test that has 4 possible answers for
each question. You get 3 points for each correct answer and lose 1 point for each incorrect answer, and do not gain or lose any points for answers left blank. If you do not know the answer to a question is it to your advantage to guess an answer to a question you don’t know?
Hint:1. Find the probability of each outcome. 2. Find the expected value of guessing the answer
Answer
1. Each question has 4 possible answers; only 1 is correct.
Guessing correctly is ¼ and guessing incorrectly is ¾
2. Multiply the points gained or lost by the correspoding probability. 3 for correct, -1 for incorrect so….
E = 3(1/4) + (-1) (3/4) = 0
¾ - ¾ = 0 so what is your answer? Is it advantageous to guess if you don’t know the answer???
Can we make money?
At a roulette wheel there are 2 zeroes and 36 non zero numbers (18 red and 18 black) to bet on. If I bet $1 on red what is the expected value of my bet?
How about after 10 of the same bets? How much can I be expected to win or lose?
Did I win?
My chance of winning $1 is 18/38 and my chance of losing $1 (or winning -$1) is 20/38.
My expected value, E = (18/38) ( 1 ) + (20/38 )( -1) = 18/38 - 20/38 = -2/38 = -5.26%. I can expect to lose .0526 every spin of the wheelAfter 10 bets I will lose 52.6 = 53 cents.
SpinnerSpinner
What is the expected value of the spinner?What is the expected value of the spinner?
$360018
$450 $1800 $800
$200
$500
$400
$700
$100
$300$600
Tables
x P
3 .25
4 .30
13 .10
2 .35
Use your formula and calculate
(.25) 3 + (.30) 4 + (.10) 13 + (.35) 2 =
.75 + 1.20 + 1.30 + .70 = 3.95
Tables Tables
Find the expected value of Find the expected value of the following event. the following event.
1
173.8
30
6.85
x P
5 .25
8 .30
11 .10
6 .35