A spinner has two sections of equal size that are numbered 2 and 4. The spinner will be spun three times.
What is the probability that the sum of the three spins is 7?
A. [tex]\frac{1}{8}[/tex]
B. [tex]\frac{2}{8}[/tex]
C. [tex]\frac{6}{8}[/tex]
D. [tex]\frac{3}{8}[/tex]
Answer (1)
List all possible outcomes: (2,2,2), (2,2,4), (2,4,2), (2,4,4), (4,2,2), (4,2,4), (4,4,2), (4,4,4).
Calculate the sum of each outcome.
Count the outcomes where the sum is 10: 3 outcomes.
Calculate the probability: 8 3 .
8 3
Explanation
Analyze the problem Let's analyze the problem. We have a spinner with two sections, labeled 2 and 4. We spin it three times and want to find the probability that the sum of the three spins is 10.
List all possible outcomes First, let's list all possible outcomes when spinning the spinner three times. Each spin can result in either a 2 or a 4. The possible outcomes are: (2, 2, 2), (2, 2, 4), (2, 4, 2), (2, 4, 4), (4, 2, 2), (4, 2, 4), (4, 4, 2), (4, 4, 4).
Calculate the sum of each outcome Next, let's calculate the sum of each possible outcome:
(2, 2, 2) = 6
(2, 2, 4) = 8
(2, 4, 2) = 8
(2, 4, 4) = 10
(4, 2, 2) = 8
(4, 2, 4) = 10
(4, 4, 2) = 10
(4, 4, 4) = 12
Count outcomes with sum of 10 Now, let's count the number of outcomes where the sum is equal to 10. From the list above, we can see that there are 3 outcomes where the sum is 10: (2, 4, 4), (4, 2, 4), and (4, 4, 2).
Total number of outcomes The total number of possible outcomes is 8, as we listed them in step 2.
Calculate the probability To find the probability that the sum of the three spins is 10, we divide the number of outcomes where the sum is 10 by the total number of possible outcomes. So, the probability is 8 3 .
Final Answer Therefore, the probability that the sum of the three spins is 10 is 8 3 .
Examples
Imagine you're designing a simple game with a spinner. This calculation helps you determine the likelihood of a player achieving a specific score, which is crucial for balancing the game's difficulty and reward system. By understanding the probabilities, you can create a game that is both engaging and fair.
