You will need an understanding of algebra and combinatorics to solve today’s challenge.
Today’s challenge begins with 3 rows of fruits. They begin with an apple, and orange, and a pear. The fruits behind the front are unknown. Directly behind any apple, there is an equal chance of a plum, a banana, or an orange. There is no other fruit directly behind an apple, but one apple is at the end of a row. Behind any plum is the same fruit that was in front of it. Directly behind an orange, there is a one third probability there are grapes. There is an equal probality of pears and blueberries, and 1 orange leads to a banana. For any banana there is an equal chance of blueberries or a plum. 1 banana is followed by grapes, and another ends a row. Behind blueberries, there is a one third chance of a pear, otherwise grapes. Directly behind grapes, there is a 50% chance of more grapes, a 25% chance of a plum, and otherwise a pear. Finally, directly behind a pear there is the fruit of the colour in the rainbow following that of the fruit in front of the pair. The exception is the 1 pear that ends a row. The apples in this question are red, which is considered to follow purple, the colour of the plums. The fruit following the pair at the front is an apple. The challenge is to use this information to find the probability that the row started by a pear ends with one.