$10 bet between you and me. At any time during the game, I can ask to double it. If you accept we both put in another $10 and if you win, you win the $20 and if you lose, you lose it all. If you reject, you lose the initial $10. What is the minimum probability you would take to accept the double

its 20 or 0

Step-by-step explanation:

Right now he has $10 and if he wins the bet he gets $20, if he loses he loses his $10 which will leave him with nothing but a 0.

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%