Question

12. A basket contains 12 fruits: orange, apple and avocado pear, all of the same size. The number of oranges, apples and avocado pears forms three consecutive integers. Two fruits are drawn one after the other without replacement. Calculate the probability that:
(a) the first is an orange and the second is an avocado pear;
(b) both are of the same fruit;
(c) at least one is an apple.

Accepted Answer

Since the counts are 3 consecutive integers summing to 12: Oranges=3, Apples=4, Avocado pears=5.
(a) P(orange then avocado pear) = (3/12)×(5/11) = 15/132 = 5/44.
(b) P(both same fruit) = (3/12×2/11)+(4/12×3/11)+(5/12×4/11) = 6/132+12/132+20/132 = 38/132 = 19/66.
(c) P(at least one apple) = 1−P(no apple) = 1−(8/12×7/11) = 1−56/132 = 19/33.

WAEC Further Mathematics 2022 Theory — Question 12

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