Question: A circular spinner is divided into 16 sectors of equal area. There are 6 red sectors, 6 blue, 2…

A circular spinner is divided into 16 sectors of equal area. There are 6 red sectors, 6 blue, 2 yellow, and 2 green. Consider the experiment of spinning the spinner once. Find the probability that the spinner lands on blue.

Let E be the event that the spinner lands on a blue sector, where the total number of outcomes in the sample space is the total number of sectors. Find the number of elements in event E, n(E), and the total number of outcomes in the sample space, n(S). n(E) = n(S) =

Solution

To solve the problem, we’ll start by identifying the number of elements in event \( E \), \( n(E) \), and the total number of outcomes in the sample space, \( n(S) \). 1. Identify \( n(S) \): The sample space \( S \) is the total number of sectors on the spinner. According to the problem, there are 16 sectors. Therefore: \[ n(S) = 16 \] 2. Identify \( n(E) \): The event \( E \) is landing on a blue sector. There are 6 blue sectors. Therefore: \[ n(E) = 6 \] 3. Find the probability that the spinner lands on blue: The probability of an event is given by the ratio of the number of successful outcomes to the total number of outcomes in the sample space: \[ P(E) = \frac{n(E)}{n(S)} = \frac{6}{16} = \frac{3}{8} \] The probability that the spinner lands on blue is \( \frac{3}{8} \).