Dans Diner employs three dishwashers Rohan washes 40

Dan’s Diner employs three dishwashers. Rohan washes 40% of the dishes and breaks only 1% of those he handles. Clara and Carlos each wash 30% of the dishes. Clara breaks only 1% of hers but Carlos breaks 3% of the dishes he washes. You go to Dan’s Diner for dinner one night and hear a dish break at the sink. What’s the probability that Carlos is the one who broke it?

1 T R A P 6 1 R E T P CHA E U L A V D E EXPECT

Game Rules: • Everybody stand up! • I’ll roll a die. You can sit down and keep the points, or stand try for higher points. • If a 5 rolls, everybody standing loses their points!

A card dealer offers you a game that costs $5 to play. If you draw the Ace of Hearts, you win $100. If you draw any other Ace, you win $10. If you draw any other Heart, you win back your $5. Any other card drawn will result in losing your $5. Would you play?

Expected Value The expected value of a random variable is its theoretical long-run average value.

Probability Model for the card game described Outcome Payout (x) Probability P(x) Ace of Hearts $100 – 5 = $95 1/52 Ace – not Heart $10 – 5 = $5 3/52 Heart – not Ace $5 – 5 = $0 12/52 Other 36/52 $0 – 5 = -$5

A restaurant offers a special that could save you a lot of money! When the waiter brings the check, he will also bring the 4 aces from a deck of cards. He’ll shuffle them and lay them face down on the table. You get to turn over one card. If it’s a black ace, you don’t win anything. If it’s the Ace of Hearts, you win a $20 discount. If it’s the Ace of Diamonds, you’ll get to turn over another card and if you then get the Ace of Hearts, you get a $10 discount. P(Ace of Hearts ) = P(Ace Diamonds then Ace of Hearts) = P(Ace Diamonds then Black Ace)= P(Black Ace)=

A restaurant offers a special that could save you a lot of money! When the waiter brings the check, he will also bring the 4 aces from a deck of cards. He’ll shuffle them and lay them face down on the table. You get to turn over one card. If it’s a black ace, you don’t win anything. If it’s the Ace of Hearts, you win a $20 discount. If it’s the Ace of Diamonds, you’ll get to turn over another card and if you then get the Ace of Hearts, you get a $10 discount. Outcome Ace Hearts x P(x) $20 Ace D then Ace H No Win (black ace) $10 $0

An insurance company offers a “death and disability” policy that pays $10, 000 when you die or $5000 if you are permanently disabled. It charges a premium of $50 a year for this benefit. Will it make a profit if the death rate in any year is 1 out of 1000 people and that another 2 out of 1000 people suffer from some kind of disability? Outcome Death Disability Neither Payout (x) 10, 000 5, 000 0 Probability P(x) 1/1000 2/1000 997/1000 If they are collecting $50 per policy and paying out an average of $20, then the profit is an average of $30 per policy per year.

Today’s Assignment: q. Read Chapter 16 q. HW: page 383 #1 -6