1. Probability of Toy Production
A toy factory has two machines. Machine 1 has a 70% probability of producing a toy, and Machine 2 has a 30% probability. If Machine 1 produces a toy, there is a 70% chance it will be a doll. If Machine 2 produces a toy, there is a 90% chance it will be a doll. Given that a toy produced is a doll, what is the probability that it was produced by Machine 2?
2. Work Payment Distribution
If one person can complete a task in 9 days, another in 6 days, and a third in 14 days, and they are paid a total of 4400, how much does the first person earn?
3. Household Items Ownership
If 60 households have a TV, 85 have a scooter, 70 have a refrigerator, and 130 households have exactly one of these items, how many households are there in total?
4. Probability of Shared Birthdays
What is the probability that, in a group of 400 people, at least two people share the same birthday?
5. Count of Numbers Divisible by 3 or 4
How many numbers within the range of 100 to 999 are divisible by 3 or 4?