# Probability of picking fruits

I am trying to answer the following question:

One apple, one banana and one cherry are blindly picked and each fruit is either ripe, unripe or rotten. Assuming that unripe, ripe or rotten fruits are equally likely to be chosen, what is the sample space?

I am doing a probability tree and coming up with a large sample of $27$ options... is this correct? or are there only $9$ options in the sample space? Eg RipeA, unripeA, RotA, ripeB, unripeB, RottenB, RipeC, unripeC, RottenC.

It's 27. The possible outcomes are triples, e.g. (RipeA, RipeB, RottenC)

Something like RipeA is not an outcome of this experiment, only a possible part of an outcome

sample space has 27 items. there are three choices for the apple: ripe, unripe, or rotten. independently, the banana and cherry similarly, also have three choices each. so sample space is 3x3x3 = 27.

Yes that is correct. Your first answer that is. There are $3$ types of fruits and $3$ categories each fruit can be in so we get $$3^3=27$$

One way to think about this is lining up the $3$ fruits which I will denote as $A$, $B$, and $C$. There are $3$ options for each of $A,B$, and $C$ being $1,2,$ and $3$ so we get $3\cdot3\cdot3=27$

Listing them out is possible as the sample is small:

$A1,B1,C1$

$A1, B2, C2$

$A1, B3, C3$

$A1, B1, C2$

$A1, B2, C1$

$A1, B1, C3$

$A1, B3, C1$

$A1, B2, C3$

$A1, B3, C2$

$A2,B1,C1$

$A2, B2, C2$

$A2, B3, C3$

$A2, B1, C2$

$A2, B2, C1$

$A2, B1, C3$

$A2, B3, C1$

$A2, B2, C3$

$A2, B3, C2$

$A3,B1,C1$

$A3, B2, C2$

$A3, B3, C3$

$A3, B1, C2$

$A3, B2, C1$

$A3, B1, C3$

$A3, B3, C1$

$A3, B2, C3$

$A3, B3, C2$