1. Warm Up
Construct a probability distribution and draw a graph for drawing a card from a deck of 40 cards consisting of 10 cards numbered #1, 10 cards numbered #2, 15 cards numbered #3, and 5 cards numbered #4.

2. From past experience, a company has found that in cartons of transistors, 92% contain no defective transistors, 3% contain one defective transistors, 3% contain two defective transistors, and 2% contain three defective transistors. Find the mean, variance, and standard deviation for the defective transistors.
About how many extra transistors per day would the company need to replace the defective ones if it used 10 cartons per day?
First, make the discrete probability distribution.

3. X
P(X)

4. About how many extra transistors per day would the company need to replace the defective ones if it used 10 cartons per day?
The average number of defective transistors per carton is 0.15, so the average number of defective transistors per ten cartons should be approximately, 10(0.15) = 1.5, Approx 2 transistors.

5. Is it really worth it. At what point is gambling “profitable”
Is it really worth it???? At what point is gambling “profitable”? These are all questions of expected value.
Expected value usually deals with $$$$ so we round to the nearest cent.
Expected value is the mean, so E(X) = μ.

6. 1500 tickets are sold at $1 each for a color television valued at $1,000. What is the expected value of the gain if a person purchases one ticket?
Win
Lose
Gain X
$999
-$1
Prob. P(X)

7. One thousand tickets are sold at $1 each for four prizes of $100, $50, $25, and $10. What is the expected value if a person purchases two tickets?
Gain X
$98
$48
$23 $8
-$2
Prob. P(X)

8. A ski resort loses $70,000 per season when it does not snow very much and makes $250,000 profit when it does snow a lot. The probability of its snowing at least 75 inches (i.e. a good season) is 40%. Find the expectation for the profit.

9. At a raffle, 1500 tickets are sold at $2 each for four prizes of $500, $250, $150, and $75. You buy one ticket. What is the expected value of your gain?

10. These are obviously examples of fund-raising type activities
These are obviously examples of fund-raising type activities. In gambling games, if the expected value of the game is zero, the game is said to be fair. If the expected value of a game is positive, then the game is in favor of the player. That is, the player has a better-than-even chance of winning. If the expected value of the game is negative, then the game is said to be in favor of the house. That is, in the long run, the players will lose money.
Notes form: In gambling, E(X) = 0 means fair game
E(X) is positive means good for player
E(X) is negative means good for house
Pgs. 238 – 239 #2, 3, 4, 6, 8, and 10 – 18 all