Question

Determine whether the following individual events are independent or dependent. Then find the probability of the combined event. Randomly selecting three sophomores for a three person committee at a high school with 34 students in each class

Answer 1

The events of selecting three sophomores for a committee from 34 students are dependent since they are chosen without replacement. The combined probability of selecting three sophomores one after the other is 1/35904.

Step-by-step explanation:

The student's question asks to determine whether the event of selecting three sophomores for a committee is independent or dependent, and then to find the probability of this combined event.

Since the students are being selected without replacement, each selection affects the outcome of the next. Thus, the events are dependent.

To calculate the probability of selecting three sophomores in succession, we can use the multiplication rule for dependent events.

For the first sophomore, the probability is 1/34, as there are 34 sophomores and we are choosing one. If one sophomore is chosen, there are now 33 sophomores left.

The probability of choosing a second sophomore is then 1/33.

Finally, with two sophomores already chosen, the probability of choosing another from the remaining 32 sophomores is 1/32.

The combined probability is the product of these individual probabilities: (1/34) * (1/33) * (1/32) = 1/35904.