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ISI2023-MCS-PCA | Question: 1

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A person throws a pair of fair dice. If the sum of the numbers on the dice is a perfect square, then the probability that the number 3 appeared on at least one of the dice is

  1. $1 / 9$
  2. $4 / 7$
  3. $1 / 18$
  4. $7 / 36$

     

2 Answers

1 1 vote
There are only two possible perfect squares 4 and 9. The cases corresponding to sum being equal to 4 are (1, 3), (2, 2), and (3, 1), where the first entry represents the number on the first die and second number on the second die, totaling 3, And that for the sum being equal to 9 we have (3, 6), (4, 5), (5, 4), and (6, 3), totaling 4.

The required case are (1, 3), (3, 1), (3, 6), and (6, 3), hence total of 4 cases.

Required probability is therefore 4/36. Option A.
1 1 vote

Possibilities to sum upto 4..
3,1
1,3
2,2
Possibilities to sum upto 9..
6,3
3,6
5,4
4,5
So, total intersections of it are 7..
So, the total number of times 3 appreas is 4 times...

Hence, P(required) = 4/7..
So, Option B is TRUE

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