"We're playing a game. Cards numbered from 1-10 are placed in a hat. whatever card is drawn is the paid out amount. how much should i charge you to play this game? If you can redraw by placing the first card back into the hat, what is the new price?"

You have 50 red marbles and 50 blue marbles. Your have two jars. If I am to choose a jar at random, what ratios of marbles would you put in each jar to increase the probability of me choosing a red marble?

Determine which jar has the heavier marbles in the least amount of weighings

You have 10 jars .Each jar has 100 marbles
9 of the 10 jars -> each marble weighs 1 gram each
last jar -> each marble weights 1.1 grams each
electronic weight scale
    - place what you want to weight on it
    - hit a button
    - get the total weight

find the defective jar ?

Answer:Take 1 marble from jar 1, 2 from jar 2, 3 from jar 3 and so on...so u have 55 marbles in all
Weigh them all together...if total weight is 55.1....then jar 1 is the one with obese marbles...if 55.2..then jar 2...and so on...  again 55.3 can't be the combination of jar 1 and 2 as (.1 +.2 ) since defective jar is only one.