Question

during game play, juan threw 2 darts onto the board. determine the likelihood of the scores juan could get with his two throws. 4 or greater: dropdown, 14: dropdown, 16: dropdown (image shows a square with three concentric circles labeled 8 pts, 4 pts, 2 pts)

Explanation:

Step1: Identify possible scores per dart

The dartboard has regions with 2 pts, 4 pts, and 8 pts. So each dart can score 2, 4, or 8.

Step2: List all possible two - dart score combinations

• First dart = 2, Second dart = 2: Total = \(2 + 2=4\)
• First dart = 2, Second dart = 4: Total = \(2 + 4 = 6\) (but we are interested in 4 or greater, and 6 is greater than 4. However, let's list all combinations for 4 or greater)
• First dart = 2, Second dart = 8: Total = \(2+8 = 10\)
• First dart = 4, Second dart = 2: Total = \(4 + 2=6\)
• First dart = 4, Second dart = 4: Total = \(4+4 = 8\)
• First dart = 4, Second dart = 8: Total = \(4 + 8=12\)
• First dart = 8, Second dart = 2: Total = \(8+2 = 10\)
• First dart = 8, Second dart = 4: Total = \(8 + 4=12\)
• First dart = 8, Second dart = 8: Total = \(8+8 = 16\)

But we need to find the likelihood (probability) of getting a total of 4 or greater, 14, and 16. Wait, maybe the problem is about the number of ways to get each score. Let's re - evaluate.

Wait, maybe the dartboard has three regions: 2 - point (outer), 4 - point (middle), 8 - point (inner). When throwing two darts, the possible scores (sums) are:

• 2 + 2 = 4
• 2+4 = 6
• 2 + 8=10
• 4+2 = 6
• 4 + 4=8
• 4+8 = 12
• 8+2 = 10
• 8 + 4=12
• 8+8 = 16

Now, let's check for each target score:

For score = 4 or greater:

All possible two - dart sums are 4, 6, 8, 10, 12, 16. The only sum less than 4 would be if we had negative scores, which we don't. Wait, no, the minimum sum is 2 + 2=4. So the number of ways to get 4 or greater: all 9 possible combinations (since there are 3 choices for first dart and 3 choices for second dart, \(3\times3 = 9\) total outcomes).

For score = 14:

Is there any combination of two darts (2, 4, 8) that sums to 14? Let's check:

• 2 + 12: 12 not a possible dart score.
• 4+10: 10 not a possible dart score.
• 8 + 6: 6 not a possible dart score. So there are 0 ways to get 14.

For score = 16:

The only combination is 8+8. So there is 1 way to get 16.

Answer:

• For "4 or greater": 9 (since all 3×3 = 9 outcomes give 4 or more)
• For "14": 0 (no combination of 2, 4, 8 sums to 14)
• For "16": 1 (only 8 + 8)