In a stack of cards, 1-fifth of the cards are blue, 3-tenths of the cards are green, 2-fifths of the cards are orange, and the rest of the cards are red. One card is chosen at random.

To find the likelihood of each color being chosen, we need to calculate the probability of choosing each color.

Given that 1-fifth of the cards are blue, we can say that the probability of choosing a blue card is 1/5.

Similarly, since 3-tenths of the cards are green, the probability of choosing a green card is 3/10.

And if 2-fifths of the cards are orange, then the probability of choosing an orange card is 2/5.

Since the remaining cards are red, the probability of choosing a red card would be 1 - (1/5 + 3/10 + 2/5) = 1 - (1/5 + 3/10 + 4/10) = 1 - (1/5 + 7/10) = 1 - (2/10 + 7/10) = 1 - (9/10) = 1/10.

Therefore, the likelihood of each color being chosen is:
- Blue: 1/5
- Green: 3/10
- Orange: 2/5
- Red: 1/10

order them from least likely to most likely

Ordering them from least likely to most likely, we have:

1. Red: 1/10 probability
2. Blue: 1/5 probability
3. Green: 3/10 probability
4. Orange: 2/5 probability

To find the likelihood of each color being chosen, we need to determine the proportion of each color in the stack of cards.

Given information:
- 1-fifth of the cards are blue, which can be written as 1/5.
- 3-tenths of the cards are green, which can be written as 3/10.
- 2-fifths of the cards are orange, which can be written as 2/5.
- The rest of the cards are red, which means the remaining proportion is 1 - (1/5 + 3/10 + 2/5).

To simplify the calculations, we can convert all fractions to have the same denominator.

1/5 = 2/10
3/10 = 3/10
2/5 = 4/10

Now, let's add up the fractions:
2/10 + 3/10 + 4/10 = 9/10

Since the total proportion of cards is 9/10, the remaining proportion for red cards is 1 - 9/10 = 1/10.

Therefore, the likelihood of each color being chosen is:
- Blue: 2/10 or 1/5
- Green: 3/10
- Orange: 4/10 or 2/5
- Red: 1/10