Answer: To calculate the probability of at least one left-handed person being selected when three people are chosen at random, we need to find the probability of the complementary event, which is the probability of selecting no left-handed persons, and then subtract it from 1.
Let's assume the probability of selecting a left-handed person (success) is P(left-handed) and the probability of not selecting a left-handed person (failure) is P(not left-handed).
Since we have no information about Jocelyn's results or the actual probabilities, let's assume the probability of selecting a left-handed person is 30% (0.30) and the probability of not selecting a left-handed person is 70% (0.70). These values are just examples for illustration purposes, and the actual values may vary based on the data.
The probability of selecting no left-handed persons in three random selections is the probability of failure (not selecting a left-handed person) in each selection, multiplied together:
P(no left-handed persons) = P(not left-handed) * P(not left-handed) * P(not left-handed)
P(no left-handed persons) = 0.70 * 0.70 * 0.70 = 0.343
Now, to find the probability of at least one left-handed person being selected, we subtract the probability of selecting no left-handed persons from 1:
P(at least one left-handed person) = 1 - P(no left-handed persons)
P(at least one left-handed person) = 1 - 0.343 = 0.657
Finally, to express the answer to the nearest whole percent, we convert the probability to a percentage:
P(at least one left-handed person) ≈ 65.7%
So, based on the assumption of a 30% probability of selecting a left-handed person, the probability of at least one left-handed person being selected when three people are chosen at random is approximately 65.7%. Please note that this value is based on the assumed probabilities and may vary if the actual probabilities are different.