A bird randomly chooses to land on 1 of 12 perches available in its aviary. Determine the Probability of it landing on a perch numbered 8 and then on a perch marked with a prime number; take into account that he never lands on the same perch in the sequence.

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Answer to a math question A bird randomly chooses to land on 1 of 12 perches available in its aviary. Determine the Probability of it landing on a perch numbered 8 and then on a perch marked with a prime number; take into account that he never lands on the same perch in the sequence.

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A probabilidade de uma ave pousar num poleiro específico é determinada pelo número total de poleiros disponíveis. Neste caso, existem 12 poleiros, então a probabilidade de o pássaro pousar no poleiro número 8 é 1/12. Os números primos menores que 12 são 2, 3, 5, 7 e 11. Portanto, existem 5 poleiros de números primos. Porém, como a ave nunca pousa no mesmo poleiro em sequência, se tiver pousado no poleiro número 8, não poderá pousar novamente no poleiro número 8. Portanto, o número total de poleiros disponíveis para a ave pousar em seguida é 11. Portanto, a probabilidade de o pássaro pousar em um poleiro de número primo após pousar no poleiro número 8 é 5/11. A probabilidade combinada é (1/12) * (5/11) = 5/132. Portanto, há uma chance de 5 em 132 de que o pássaro pouse no poleiro número 8 e depois em um poleiro marcado com um número primo.

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