Isaac has made two fair spinners. Spinner 1 has 10 equal sized sections. Spinner 2 has 4 equal sized sections.
Isaac says:
"It is more likely to get a 4 on spinner 1 than spinner 2 because there are two number [tex]$4 s$[/tex] on spinner 1 and only one number 4 on spinner 2 ."
Explain why Isaac is incorrect.
Answer (1)
Calculate the probability of getting a 4 on Spinner 1: 10 2 = 5 1 .
Calculate the probability of getting a 4 on Spinner 2: 4 1 .
Compare the probabilities: \frac{1}{5}"> 4 1 > 5 1 .
Isaac is incorrect because he didn't consider the total number of sections on each spinner. It is more likely to get a 4 on Spinner 2. I s aa c i s in correc t
Explanation
Analyze Isaac's Statement Let's analyze Isaac's statement. He believes that having more '4's on Spinner 1 makes it more likely to land on a 4 compared to Spinner 2. However, we need to consider the total number of sections on each spinner to determine the actual probabilities.
Calculate Probability for Spinner 1 To find the probability of landing on a 4 on Spinner 1, we divide the number of sections with a 4 by the total number of sections. Spinner 1 has two sections with a 4 and a total of 10 sections. So, the probability of landing on a 4 on Spinner 1 is: 10 2 = 5 1
Calculate Probability for Spinner 2 Now, let's calculate the probability of landing on a 4 on Spinner 2. Spinner 2 has one section with a 4 and a total of 4 sections. So, the probability of landing on a 4 on Spinner 2 is: 4 1
Compare the Probabilities Comparing the two probabilities, we have: Probability of 4 on Spinner 1: 5 1 Probability of 4 on Spinner 2: 4 1
To easily compare these fractions, we can convert them to have a common denominator. The least common denominator for 5 and 4 is 20. So, 5 1 = 20 4 4 1 = 20 5 Since \frac{4}{20}"> 20 5 > 20 4 , the probability of landing on a 4 is higher on Spinner 2 than on Spinner 1.
Explain Why Isaac is Incorrect Isaac is incorrect because he only considered the number of sections with a 4 on each spinner and didn't take into account the total number of sections. Probability depends on the ratio of favorable outcomes to the total number of possible outcomes. Spinner 2 has a higher probability of landing on a 4 because \frac{1}{5}"> 4 1 > 5 1 .
Final Answer Therefore, it is more likely to get a 4 on Spinner 2 than on Spinner 1.
Examples
Understanding probability is crucial in many real-life scenarios, such as when playing games of chance, making investment decisions, or even understanding weather forecasts. For instance, if you're playing a game with dice, knowing the probability of rolling a certain number can help you make strategic decisions. Similarly, in finance, understanding the probability of different market outcomes can guide investment strategies to minimize risk and maximize potential returns. This problem illustrates the importance of considering all possible outcomes when assessing probabilities, rather than focusing on only one aspect of the situation.
