A spinner is divided into 4 sections of equal size labeled with the numbers 1, 2, 3, and 4. You spin it 3 times and get the following results: 1, 4, 3. Which of the following is true?
The theoretical probability of getting a 1 is 25%.
The experimental probability of getting a 1 is 25%.
If you spin the spinner again and get different results, the theoretical probability will change.
All of the above are true.
What do you think the theoretical probability of a one is?
theoretical prob of getting 1 is 25%
To determine which of the statements is true, we need to understand the difference between theoretical and experimental probability.
Theoretical probability is the likelihood of an event occurring based on mathematical calculations. In this case, since the spinner is divided into 4 equal sections, the probability of landing on any specific number is 1 out of 4 or 25%.
Experimental probability, on the other hand, is determined through actual experimentation or observation. It is calculated by dividing the number of times an event occurs by the total number of trials. In this case, the experimental probability of getting a 1 would be the number of times 1 appears in the 3 spins divided by 3.
Now let's analyze the statements one by one:
1. The theoretical probability of getting a 1 is 25%.
This statement is true because, as mentioned earlier, there is only one section on the spinner labeled with a 1, out of a total of 4 sections, resulting in a 25% (1/4) chance of landing on 1.
2. The experimental probability of getting a 1 is 25%.
To verify this statement, we need to see if the number 1 appeared in the 3 spins. Since the sequence of spins was mentioned as 1, 4, 3, the number 1 did appear once. Therefore, the experimental probability of getting a 1 is 1 out of 3 or 33.33% (approximately), not 25%. Hence, this statement is false.
3. If you spin the spinner again and get different results, the theoretical probability will change.
This statement is untrue. The theoretical probability remains constant, regardless of the outcomes in previous spins. In this case, the theoretical probability of getting a 1 will always be 25%, regardless of the results of any previous spins.
Given the analysis above, we can conclude that statement 1 is true, statement 2 is false, and statement 3 is false. Therefore, the correct answer is: "The theoretical probability of getting a 1 is 25%."