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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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
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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