1. Torpedo question: 2 torpedoes, each with 1/3 probability of hitting/ sinking a ship
2. I have 20% chance to have cavity gene. If I do have the gene, there is 51% chance that I will have at least one cavity over 1 year. If I don’t have the gene, there is 19% chance that I will have at least one cavity over 1 year. Given that I have a cavity in 6 months, what’s the probability that I have at least a cavity over 1 year?
3. What is the probability of 5 people with different ages siting in ascending or descending order at a round table?
4. We are racing, and can at any time signal to the other that we would like to double our bet. We've put down 100 to start and during the race I signal to you I want to double the bet, What is the minimum probability of winning for you to accept to continue?
5. Candy bar A produces 60% market's candy, of which 20% is damaged. Candy Bar B produces 40% of the markets candy, of which 10% is damaged. Given that you see a damaged candy bar, what is the probability that its Candy Bar B?
6. The probability of seeing a shooting star in 1 hour is 91%. What is the probability of seeing a shooting star in 30 minutes?
Variation: If there is an 84% chance of an event happening in an hour, what is the probability that it happens in half an hour?
7. You have are offered a contract on a piece of land which is worth 1000000 70% of the time, 500000 20% percent of the time and 150000 10% of the time. The contract says you can pay x dollars for someone to determine the land's value from where you can decide whether or not to pay 300000 for the land. What is x? I.e. how much is this contract worth?
Variation: A piece of land has a 30% chance of being located over an oil reserve, in which case it is going to be worth 100M. If there is no oil, the land is worth 30M. You are offered an option to buy the land at 40M after inspecting it and ascertaining if there is oil. How much are you willing to pay for this option?