We are given that 9% of people are left-handed, which means the probability of selecting a left-handed person is $p = 0.09$. The probability of selecting a right-handed person is $1 - p = 0.91$. We are asked to find the probability that there are some left-handed people among 6 randomly selected individuals.

This is a binomial probability problem where:

• The number of trials $n = 6$,
• The probability of success (selecting a left-handed person) $p = 0.09$,
• The probability of failure (not selecting a left-handed person) $1 - p = 0.91$.

Step 1: Complementary Probability Approach

The easiest way to find the probability that there are some left-handed people is to use the complement rule. First, we calculate the probability that none of the 6 people are left-handed, then subtract this value from 1 to find the probability that at least one person is left-handed.

The probability that none of the 6 people are left-handed is: $P(\text{none left-handed}) = (0.91)^6$

Now, calculate this: $P(\text{none left-handed}) = 0.91^6 \approx 0.606$

Step 2: Find the Probability of "Some Left-Handed"

The probability of having some left-handed people is the complement of the probability that none are left-handed: $P(\text{some left-handed}) = 1 - P(\text{none left-handed})$ $P(\text{some left-handed}) = 1 - 0.606 = 0.394$

Thus, the probability that there are some left-handed people among the 6 selected is approximately 0.394, or 39.4%.

Would you like more details or further questions?

Here are 5 related questions to explore:

1. What is the probability that exactly 2 of the 6 people are left-handed?
2. What is the probability that all 6 people are right-handed?
3. How does the binomial distribution change if the probability of being left-handed increases to 20%?
4. How many left-handed people would you expect to find among 10 randomly selected people?
5. What is the probability that fewer than 3 people are left-handed among 8 selected individuals?

Tip: The complement rule is often helpful when finding the probability of "at least one" event happening!