A 5-sided spinner is numbered [tex]$1,2,3,4,5$[/tex]. The table below shows the probability of the spinner landing on [tex]$1,2,3,4$[/tex]. Complete the table.
| Number | 1 | 2 | 3 | 4 | 5 |
| --- | --- | --- | --- | --- | --- |
| Probability | 0.27 | 0.18 | 0.32 | 0.12 | [tex]$x$[/tex] |
Answer (2)
To find the probability of landing on number 5 from the spinner, we calculated the total of the provided probabilities and subtracted that from 1. The resulting probability for landing on 5 is 0.11. This ensures that the total probabilities of all outcomes equal 1, as required in probability theory.
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The sum of probabilities of all outcomes equals 1.
Express the equation: 0.27 + 0.18 + 0.32 + 0.12 + x = 1 .
Solve for x : x = 1 − ( 0.27 + 0.18 + 0.32 + 0.12 ) .
The probability of landing on 5 is: 0.11 .
Explanation
Analyze the problem and data Let's analyze the problem. We have a 5-sided spinner with known probabilities for landing on the numbers 1, 2, 3, and 4. We need to find the probability, denoted as x , for the spinner landing on the number 5. The fundamental principle we'll use is that the sum of probabilities for all possible outcomes of an experiment must equal 1.
Set up the equation Now, let's set up the equation. The sum of the probabilities for landing on 1, 2, 3, 4, and 5 must equal 1. So, we have:
0.27 + 0.18 + 0.32 + 0.12 + x = 1
Isolate x Next, we need to solve for x . To do this, we'll subtract the known probabilities from 1:
x = 1 − ( 0.27 + 0.18 + 0.32 + 0.12 )
Calculate x Now, let's calculate the value of x :
x = 1 − ( 0.27 + 0.18 + 0.32 + 0.12 ) = 1 − 0.89 = 0.11
State the final answer Therefore, the probability of the spinner landing on 5 is 0.11.
Examples
Imagine you're designing a game with a spinner, and you want to ensure the probabilities of landing on each section add up to 1 (or 100%). This problem demonstrates how to calculate the missing probability for one of the sections, given the probabilities of the others. For example, if you know the probabilities of landing on sections 1, 2, 3, and 4 are 0.27, 0.18, 0.32, and 0.12, respectively, you can calculate the probability of landing on section 5 to be 0.11, ensuring a balanced and fair game.
