Question

practice

1. linh received a dart board for his birthday. the rule book says that two darts are to be thrown and that an individuals score is the sum of the two numbers.

a. complete an array to determine all the outcomes for obtaining the sums.

b. list the sample space for the sum of the numbers.

c. are all outcomes equally likely? explain your reasoning.

Explanation:

Step1: Verify array sums

Each cell = row value + column value:

• Row 2: $2+2=4$, $2+4=6$, $2+6=8$, $2+8=10$
• Row 4: $4+2=6$, $4+4=8$, $4+6=10$, $4+8=12$
• Row 6: $6+2=8$, $6+4=10$, $6+6=12$, $6+8=14$
• Row 8: $8+2=10$, $8+4=12$, $8+6=14$, $8+8=16$

Step2: Identify unique sums

Extract distinct values from the array: $4,6,8,10,12,14,16$

Step3: Count sum frequencies

• 4: 1 occurrence, 6: 2 occurrences, 8: 3 occurrences, 10: 4 occurrences, 12: 3 occurrences, 14: 2 occurrences, 16: 1 occurrence

Answer:

a. The completed array (corrected/verified) is:

Dart 1\Dart 2	2	4	6	8
4	$4+2=6$	$4+4=8$	$4+6=10$	$4+8=12$
6	$6+2=8$	$6+4=10$	$6+6=12$	$6+8=14$
8	$8+2=10$	$8+4=12$	$8+6=14$	$8+8=16$

b. $S = \{4, 6, 8, 10, 12, 14, 16\}$

c. No. The sums have different frequencies (e.g., 10 occurs 4 times, while 4 only occurs 1 time), so they are not equally likely.