To find the probability that at least one of two randomly selected people will consider themselves lucky, we can use the concept of complementary probability. The complementary event to "at least one considers themselves lucky" is "neither of them considers themselves lucky."

Step-by-Step Solution:

1. Probability that a person considers themselves lucky:
   Given that 10% of people in Western countries consider themselves lucky, the probability that a randomly selected person considers themselves lucky is:
   $P(\text{Lucky}) = 0.10$

2. Probability that a person does not consider themselves lucky:
   The probability that a randomly selected person does not consider themselves lucky is the complement of 0.10:
   $P(\text{Not Lucky}) = 1 - 0.10 = 0.90$

3. Probability that neither of the two people considers themselves lucky:
   If we select two people, and both do not consider themselves lucky, the probability is: $P(\text{Neither Lucky}) = P(\text{Not Lucky}) \times P(\text{Not Lucky}) = 0.90 \times 0.90 = 0.81$

4. Probability that at least one person considers themselves lucky:
   The probability of the complementary event (at least one person is lucky) is: $P(\text{At least one Lucky}) = 1 - P(\text{Neither Lucky}) = 1 - 0.81 = 0.19$

Final Answer:

$P(\text{At least one Lucky}) = 0.190$

So, the probability that at least one of the two people will consider themselves lucky is 0.190.

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Would you like more details or have any questions about the solution?

Here are 5 related questions for further exploration:

1. What is the probability that both people consider themselves lucky?
2. How would the probability change if 20% of people considered themselves lucky?
3. If 5 people are selected, what is the probability that at least one will consider themselves lucky?
4. How would you calculate the probability that exactly one person considers themselves lucky from a group of two?
5. What is the relationship between the probability of a person being lucky and the probability of at least one person being lucky in a group?

Tip: To calculate probabilities for "at least one" events, it’s often easier to find the complementary event (none of them) and subtract that probability from 1.