A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest in any one of the sectors numbered 1, 2, 3, 4, 5, 6, 7 or 8 as shown. Two such disks are used in a game where their arrows are independently spun. What is the probability that the sum of the numbers on the resulting sectors upon spinning the two disks is equal to 8 after the arrows come to rest?
Reconstructed schematic — two independent 8-sector spinner disks, sectors numbered 1–8 (Q.7).
Options:
(A) 1/16
(B) 5/64
(C) 3/32
(D) 7/64
Official Answer Key:
D
Step-by-Step Solution & Explanation
• Total equally likely outcomes = 8 × 8 = 64.
• Favourable outcomes: pairs (a,b), a,b∈{1..8}, a+b=8: (1,7),(2,6),(3,5),(4,4),(5,3),(6,2),(7,1) — 7 outcomes.
• Probability = 7/64.
• Distractor logic: (A)=4/64 misses 3 pairs; (B) and (C)=6/64 each miss one valid pair (commonly the (4,4) case).
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