Question

use the spinner below to answer the questions:
p(spinning 1) =
p(odd #) =
p(3) =
p(number less than 3) =
you spin the spinner above 400 times. how many times do you predict the spinner would land on the number 2? why?

Explanation:

Step1: Determine total number of sections

The spinner is divided into 8 equal - sized sections. So, the total number of possible outcomes \(n = 8\).

Step2: Calculate \(P(\text{spinning }1)\)

There are 2 sections labeled 1. Using the probability formula \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\), we have \(P(1)=\frac{2}{8}=\frac{1}{4}\).

Step3: Calculate \(P(3)\)

There are 3 sections labeled 3. So, \(P(3)=\frac{3}{8}\).

Step4: Calculate \(P(\text{odd \#})\)

The odd - numbered sections are the sections labeled 1 and 3. There are \(2 + 3=5\) odd - numbered sections. Then \(P(\text{odd \#})=\frac{5}{8}\).

Step5: Calculate \(P(\text{number less than }3)\)

The numbers less than 3 are 1 and 2. There are \(2+3 = 5\) sections (2 sections labeled 1 and 3 sections labeled 2). So, \(P(\text{number less than }3)=\frac{5}{8}\).

Step6: Predict the number of times landing on 2

There are 3 sections labeled 2. The probability of landing on 2 is \(P(2)=\frac{3}{8}\). If the spinner is spun \(N = 400\) times, using the formula \(n = N\times P(2)\), we get \(n=400\times\frac{3}{8}=150\).

Answer:

\(P(\text{spinning }1)=\frac{1}{4}\), \(P(3)=\frac{3}{8}\), \(P(\text{odd \#})=\frac{5}{8}\), \(P(\text{number less than }3)=\frac{5}{8}\), and if spun 400 times, it would land on 2 about 150 times.