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The total probability of getting any of the three fruits must add up to 1.
Therefore, let x be the probability of getting an orange.
5/12 (Banana probability) + 1/6 (Pear probability) + x = 1
5/12 + 1/6 + x = 1
(x = 1 - 5/12 - 1/6)
(x = 12/12 - 5/12 - 2/12)
(x = 5/12)
So, the probability of getting an orange is 5/12.