Shubham Singh

1. You roll a fair 6-sided die twice. Calculate the probability that the value of the first roll is strictly less than the value of the second roll.

Hint: Draw the table of outcomes, Solution

2. You have a pile of 100 coins. 1 of the coins is an unfair coin and has heads on both sides. The remaining 99 coins are fair coins. You randomly select a coin from the pile and flip it 10 times. The coin lands heads all 10 times. Calculate the probability that the coin you selected is the unfair coin.

Hint: Baye's Theorem, Solution

3. Suppose you and I are playing a game, and it could be any game. We have bet 10 dollars which would go to the winner. At some point, I offer to double the bet to 20 dollars. If you accept, the game continues with the new bet. If you refuse. you lose the game, along with the original ten dollars. What is the minimum probability of winning the game that you would need to accept the increased bet?

Hint: To play the increased bet, gain/loss should be more than gain/loss by not playing. Solution