SIG Questions

SIG Questions If we play a game in which Player 1 picks a number 1-11, and then player 2 can add 1-11 to that (i.e. player 1 picks 5, player 2 can add to make it 6-16), what is the strategy to win this game if Player 1 wants to make 60? 2nd, make multiples of 12 If i toss 3 pieces on a tic-tac-toe board at random, and I pay you $9 if the pieces create tic-tac-toe, and you pay me $1 if they dont, do you want to play the game? (Expected value problem) 2/21- (9*8*7)/(3*2) You know there are 2 boys and an unknown number of girls in a nursery at a hospital. Then a woman gives birth a baby, but you dont know its gender, and it is placed in the nursery. Then a nurse comes in a picks up a baby and it is a boy. Given that the nurse picks up a boy, what is the probability that the woman gave birth to a boy? (Hint, it does not matter how many girls are in the nursery to begin with) 3/5 If there is an 84% chance of an event happening in an hour, what is the probability that it happens in half an hour? What is the fair price for a dice game in which you receive the amount you roll but have the option of rolling the dice a second time. If you choose to roll a second time, you must take the amount you roll on that occasion. .5(3.5) + .5(5)= 1.75+2.5 = 4.25 You can hold a party only if there is no rain on either saturday or sunday. The probability of rain on a saturday is 80% and 60% for sunday. What is the probablity you can hold a party at the weekend? Given that you held a party, what is the probability that that it rained at the weekend? 1: 52% 2: 44/52= 11/13 You own land that may or may not have oil underneath. If it does have oil it is worth 100k (20% prob), if it doesn't it is worth 30k. What is the expected value of the land? How much would you sell a contract for this land with a strike of 40k? 44k I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. Is this game worth playing?

Probability of winning are 20/64- play the game 6 people sitting at a round table. What is a probability that they are in height order? (2/5)*(1/4)*(1/3)*(1/2) You are the captain of a submarine. You have two torpedoes. Each torpedo hits a ship independently with probability 1/3. What's the probability you will hit a ship? 1-(2/3)*(2/3)= 5/9

You are the captain of that same submarine. You can see a sinking ship on the horizon. What's the probability both of your torpedoes hit the ship? 1/9 If you flip a coin until you decide to stop and you want to maximize the ratio of heads to total flips, what is that expected ratio? 75%??? You have five pirates, ranked from 5 to 1 in descending order. The top pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. How will the coins end up being divided, assuming all the pirates are rational and want to end up alive? Do What is the expected value to you of the following game: You and another person have 3 coins each. You both flip all of your coins and if your three coins show the same number of tails as the other person, you pay them $2, otherwise they pay you $1.

If the chances of you seeing a shooting star outside within one hour is 84 percent, what is the chance of you seeing at least one shooting star outside in 30 minutes? Chances of not seeing in 60 minutes is .16, so chances of not seeing in 30 minutes is .4. So chances of seeing in 30 minutes is 60%

Two people take turns counting to 50. Each person can add from 1 to 10 to the total sum. The first to count the number 50 wins. What is your strategy? Do you want to go first? Go first, say 6, then 17, 28, 39, you WIN!!

We each flip three fair coins. I offer to pay you $1 if we do not get the same amount of heads, if you agree to pay me $2 if we do (get the same amount of heads). Will you agree to play this game? 2/3 chance of hitting a target, what is the chance of hitting it if you fire twice. 1-(1/3)^2= 1-(1/9)= 8/9