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GATE 2022 CH – Question 7

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

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?

two identical circular disks, each divided into eight equal sectors numbered 1 to 8, with an arrow at the centre.
  1. $\frac{1}{16}$
  2. $\frac{5}{64}$
  3. $\frac{3}{32}$
  4. $\frac{7}{64}$

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Correct answer: (D) $\frac{7}{64}$

Explanation

There are $8 \times 8 = 64$ equally likely outcomes. The pairs with the sum 8 are (1,7), (2,6), (3,5), (4,4), (5,3), (6,2) and (7,1), which is 7 pairs, so the probability is $\frac{7}{64}$.