Question

basket contains four apples and five peaches. Three times, you randomly select a piece of fruit, return it to the basket, and then mix the fruit. The first time, you get an apple. Then second and third times, you get peaches. Find the probability of this occuring.A. 1/32B. 25/546C. 100/729D. 8/125

Answer 1

Since the basket contains four apples and five peaches, it contains a total of nine fruits.

The first fruit we picked was an apple. The probability of this happening is the number of apples divided by the total number of fruits in the basket. In other words, the probability is 4/9.

The second and third time we picked a peach. Again, the probability of this happening is the number of peaches divided by the total number of fruits in the basket, that is, 5/9.

Since we are putting the fruit back in the basket and mixing them each time we pick one, we can consider the three events: picking an apple, picking a peach and picking another peach, to be independent events, because the result of the previous picking does not influence the result of the next picking.

As a result, the probability of this particular event happening is the multiplication of the probabilities we obtained earlier. In other words:

`P=(4)/(9)\cdot(5)/(9)\cdot(5)/(9)=(4\cdot5^2)/(9^3)=(4\cdot25)/(729)=(100)/(729)`

So, the correct answer is option C.