1. Marbles in Bags
You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble. You pick a random bag and take out one marble. It is a white marble.
What is the probability that the remaining marble from the same bag is also white?
Solution to Marbles in Bags:
Ans: Did you guess 1/2? It is actually 2/3! How do we see this?
You know that you do not have Bag B (two black marbles) so there are three possibilities:
. You chose one white marble from Bag A. The other marble will be white.
. You chose the second white marble from Bag A! This is what you may have missed: you are choosing marbles, not bags. The other marble will be white
. You chose the one white marble from Bag C. The other marble will be black.
So 2 out of 3 possibilities are white.
From: https://www.mathsisfun.com

2. Four adventurers and a small canoe
Four adventurers (Adam, Bhavani, Chak and Dara) need to cross a river in a small canoe (small boat). The canoe can only carry 100 kg.
Adam weighs 90 kg, Bhavani weighs 80 kg, Chak weighs 60 kg and Dara weighs 40 kg, and they have 20 kg of supplies.
How do they get across?
Solution to Four adventurers and a small canoe:
Clearly there has to be more than one trip. For the canoe to be brought back, therefore, two people must go across and one should return with the canoe. The lightest two, Chak and Dara, with total weight 100 kg, row across. The other combinations are too heavy. Obviously, the lightest adventurer, Dara, returns.
Now the heaviest person, Adam, rows over, and stays on the other side. The lighter person, Chak, returns.
Notice that the two lightest people, Chak and Dara, are now on the same (first) side. They both row across again, and again Dara returns.
By now you must have got the idea. Bhavani rows across with the supplies, and Chak returns. Chak and Dara row across again for the last time, but you may have realised that they can now ferry any number of people across this way.
From: https://www.mathsisfun.com