A basket contains four apples and five peaches. Three times, you randomly select piece of fruit, returning to the basket, and then mix in the fridge. The first time you get to an apple. Then second and third times you get peaches. Find the probability of this occurring

Question

Eugene Cross

Mathematics

13 February, 20:22

A basket contains four apples and five peaches. Three times, you randomly select piece of fruit, returning to the basket, and then mix in the fridge. The first time you get to an apple. Then second and third times you get peaches. Find the probability of this occurring

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Answers (1)

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Kelvin Meadows · Answer 1

100/729

Step-by-step explanation:

The basket contains 9 fruits: 4 apples and 5 peaches. Thus the probability of choosing one fruit can easily be determined.

P (Apple is selected) = number of apples / number of fruits = 4/9.

P (Peach is selected) = number of peaches / number of fruits = 5/9.

If the replacement is allowed, then the probabilities will remain unchanged for all the fruits. Therefore, the probability of selecting an apple in the any attempt is 4/9 and the probability of selecting a peach in any attempt is 5/9. Assuming that the selection of the fruits is independent, we can safely multiply the probabilities. Therefore, 4/9 * 5/9 * 5/9 = 100/729.

Therefore, the correct answer is 100/729!