Fred was almost done packing for the day, with five packages left. Unfortunately, Fred dropped the labels and had no idea which label went to which package. What is the probability that Fred managed to correctly label exactly four of the five packages?
Zero. If Fred had correctly labeled four packages, the fifth label would belong to the fifth package and all packages would be correctly labeled. Therefore it is impossible to mislabel exactly four packages.
Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.
Which is more probable?
1) Linda is a bank teller.
2) Linda is a bank teller and is active in the feminist movement.
Most people guess number two, but the probability of two events occurring together is always less than or equal to the probability of either one occurring alone. This problem is known as the Conjunction Fallacy.
Five kinds of flowers grow in separate gardens on five different streets. Here is what you know:
1. The Smiths do not grow violets.
2. The Morgans grow peonies and do not live on 2nd street.
3. The Parks live on 3rd street.
4. Begonias bloom on 4th street.
5. Roses do not grow on 5th street.
6. The Johnsons do not live on 1st street.
7. The Rosens do not grow daffodils
8. The Johnsons grow roses
9. Daffodils grow on 1st street
Which flowers grow on in whose gardens on what streets?
A dad offered to pay his son $5 for every correct answer on his math test. His son said he would pay his Dad $8 for every incorrect answer. There were 26 questions on the test and no money was exchanged.
The son got 16 questions correct and missed 10. This means he owed his Dad 10 * $8 = $80, but his Dad owed him 16 * $5 = $80, so it was a wash.
Two math equations to solve it are x + y = 26 and 5x = 8y.