Question

According to recent figures from the U.S. Census Bureau, the percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26.0% in Los Angeles. If one person is selected from each city, what is the probability that all of them are under 18? Is this an unusual event?

Please calculate the probability that all selected individuals are under 18 and determine if this event is unusual.

Answer 1

The probability of selecting individuals under 18 from all three cities (New York, Chicago, and Los Angeles) is approximately
`1.574%` which is considered an unusual event due to its low probability.

Step-by-step explanation:

When calculating the probability that all selected individuals from each city are under
`18`, we use the percentages given by the U.S. Census Bureau and multiply the individual probabilities of selecting a person under
`18` from each city. For New York City, the percentage is
`23.5%`, for Chicago it is
`25.8%`, and for Los Angeles, it is
`26.0%`. Expressing these percentages as decimals, we have:

• New York City:
  `0.235 (23.5%)`
• Chicago:
  `0.258 (25.8%)`
• Los Angeles:
  `0.260 (26.0%)`

The probability of selecting a person under 18 from all three cities is found by multiplying these probabilities:

`0.235 (NYC) × 0.258 (Chicago) × 0.260 (LA) = 0.0157417, or about 1.574%`

This event, having all selected individuals under 18, has a probability of approximately
`1.574%,` which can be considered unusual because it is relatively low. Generally, an event with a probability of less than
`5%`is regarded as unusual.