Answer: There are a few different ways to approach this problem, but one common method is to use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, we want to find the probability of at least one psychologist being chosen, which is the same as 1 minus the probability of no psychologists being chosen.
To find the probability of no psychologists being chosen, we first need to calculate the total number of ways to choose 3 people from a group of 54, which is:
54 choose 3 = 54! / (3! * 51!) = 19,958
Then we need to find the number of ways to choose 3 psychiatrists from a group of 24, which is:
24 choose 3 = 24! / (3! * 21!) = 1,344
Now, we can use these values to calculate the probability of no psychologists being chosen:
P(no psychologists) = (24 choose 3) / (54 choose 3) = 1,344 / 19,958 = 0.067 or 6.7%
Finally, we can use the complement rule to find the probability of at least one psychologist being chosen:
P(at least one psychologist) = 1 - P(no psychologists) = 1 - 0.067 = 0.93 or 93%
So the probability that at least one psychologist is chosen from the conference is 93%
Explanation: