Four cards are placed in front of you on the table, each with a number on one side and a color on the other. The visible cards show 3, 8, red and brown. Which cards should you turn over in order to test the truth of the statement that if a card shows an even number on one face, then its opposite face is red?
You’d need to turn over only the 8 and brown card. Only a card with an even number on one face and which is not red on the other face can invalidate the stated rule. If you turn over the 3 card and it’s not red, it doesn’t invalidate the rule, nor does turning over the red card and finding it has the label 3.
This test was devised by Peter Cathcart Wason and is known as the Wason selection task. Less than 10% of test subjects got it correct in two separate studies.
A necessity to some, a treasure to many, I’m best enjoyed among pleasant company. Some like me hot, some like me cold. Some prefer mild, some like me bold.
I appear in the morning but am always there. You can never see me though I am everywhere. By night I am gone, though I sometimes never was. Nothing can defeat me but I am easily gone.
You’re waiting to board your flight at the airport with 99 other passengers, each with an assigned seat. All but one of the passengers will gladly sit in their designated seat. The only exception is Randall, a scoundrel who refuses to follow the rules. When he boards, he will choose a random, unoccupied seat.
If a rule-following passenger finds someone in their spot, they will choose another one at a random from the remaining unoccupied seats.
What is the probability that the last person to board the plane will sit in their proper seat?
The randomness stops as soon as someone else sits in Randall’s assigned seat. The chances of this happening range from 1 out of 99 to 1 out of 1 (when only one seat remains).
Thus, the probability of the last person sitting in their own seat can be calculated as 1/99 plus the sum of 2 to 98 of the formula 1 / n × (n + 1), which works out to 0.5, or 50%.
So there’s a 50% chance the last passenger will sit in their own seat thanks to Randall for screwing up order and procedure when boarding an aircraft.
