In a class of seven students, a teacher spins a seven-sectored spinner (with equal-sized sectors) to determine which students to ask questions. Determine about how many times a student can expect to be called on when 100 questions are asked.
1/7 of the 100 questions, or 14-15 times.
From a set of eight marbles, five red and three white, we choose one at random. What are the odds in favor of choosing a red marble?
same kind of idea. Think of a spinner which is 5/8 red and 3/8 white. If you spin it, you will likely hit red 5/8 of the time.
Looking at the marbles, 5 of the 8 are red, so if you grab one, it will probably be red (5/8 of the time)
To determine how many times a student can expect to be called on when 100 questions are asked, we need to calculate the probability of a student being selected each time a question is asked, given that there are seven students in the class and a seven-sectored spinner.
The probability of a student being selected is equal to the ratio of the favorable outcomes (the number of times a student can be called on) to the total number of possible outcomes.
1. Start by finding the probability of a student being selected in a single spin of the spinner. Since there are seven sectors on the spinner, each representing a different student, the probability of a specific student being selected is 1 out of 7 or 1/7.
2. Since the spinner is spun for each of the 100 questions, the probability of a student being selected for each question is independent. Therefore, the probability for each question remains the same.
3. Calculate the expected number of times a student can be called on by multiplying the probability of a student being selected (1/7) by the total number of questions asked (100).
Expected number of times a student can be called on = (1/7) * 100 = 100/7 ≈ 14.29
Hence, a student can expect to be called on approximately 14.29 times when 100 questions are asked.