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Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is  
  • a)
    1/9
  • b)
    2/9
  • c)
    1/3
  • d)
    4/9 
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Two dice are thrown simultaneously. The probability that the product o...
Dice has 1-6 numbers.
Perfect square pairs = (1,1), (2,2), (1,4), (4,1), (3,3), (4,4), (5,5), (6,6)=8pairs
Total pairs possible = 6^#throws = 36
Answer : 8/36 = CORRECT OPTION IS B.
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Most Upvoted Answer
Two dice are thrown simultaneously. The probability that the product o...
The outcome of dice are, (1,1),(1, 4), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), ( 4,1).therefore, n(p) =8
total n(S)=36
n(S)/n(p)=8/36=2/9
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Community Answer
Two dice are thrown simultaneously. The probability that the product o...

Probability of the product of the numbers appearing on the dice being a perfect square

The product of the numbers on the dice will be a perfect square if one or both of the dice show numbers which are perfect squares (1, 4, or 9).

Possible outcomes for each dice
- For each dice, there are 3 possible outcomes that result in a perfect square product: 1, 4, and 9.
- Total possible outcomes for each dice = 6 (numbers 1 to 6)

Total outcomes for both dice
- Total outcomes when both dice are thrown = 6 x 6 = 36

Favorable outcomes for a perfect square product
- There are 2 dice, so the favorable outcomes for a perfect square product are when at least one of the dice shows a perfect square number.
- Favorable outcomes = 2 (one die shows a perfect square) + 1 (both dice show perfect squares) = 3

Probability calculation
- Probability = Favorable outcomes / Total outcomes = 3 / 36 = 1/12 = 2/9

Therefore, the probability that the product of the numbers appearing on the dice is a perfect square is 2/9.
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Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is a)1/9b)2/9c)1/3d)4/9Correct answer is option 'B'. Can you explain this answer?
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