Math Problem Statement

There are 5 colours on a spinner. This table shows the probabilities of landing on different colours. Find the probability of landing orange and red are equally likely. Find the probability of not landing on red.

Solution

The question asks to find the probability of not landing on red, and it provides the probabilities of landing on different colors for a spinner.

From the table:

  • Probability of landing on blue = 35%
  • Probability of landing on green = 10%
  • Probability of landing on yellow = 25%
  • Probability of landing on red = (unknown)
  • Probability of landing on orange = (unknown)

The problem mentions that the probabilities of landing on orange and red are equally likely. Therefore, the probability of landing on orange is the same as the probability of landing on red.

Step 1: Calculate the probability of colors provided.

The total probability must add up to 100%. So, let's sum the probabilities of blue, green, and yellow:

35%+10%+25%=70%35\% + 10\% + 25\% = 70\%

This leaves 30% of the probability for both orange and red combined.

Step 2: Assign probabilities to orange and red.

Since orange and red are equally likely, we divide the remaining 30% equally between them:

Probability of landing on orange=Probability of landing on red=30%2=15%\text{Probability of landing on orange} = \text{Probability of landing on red} = \frac{30\%}{2} = 15\%

Step 3: Probability of not landing on red.

To find the probability of not landing on red, we subtract the probability of landing on red from 100%:

100%15%=85%100\% - 15\% = 85\%

Thus, the probability of not landing on red is 85%.

The correct answer is 85%.


Would you like further details or have any questions?

Here are 5 related questions to explore:

  1. What is the probability of landing on a color other than orange?
  2. How would the probabilities change if the number of colors on the spinner increased to 6?
  3. What would happen to the probabilities if blue became twice as likely as red?
  4. How can probabilities be used in other types of games of chance, such as dice?
  5. What is the difference between independent and dependent events in probability?

Tip: Probabilities always sum to 100%. This can help check your work in multi-step problems like this one.

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Math Problem Analysis

Mathematical Concepts

Probability
Basic Arithmetic

Formulas

Total Probability = 100%
Equal Distribution of Probability

Theorems

Law of Total Probability

Suitable Grade Level

Grades 6-8