I am reading about Bayes Theorem where the sample example used is:
We have a red box with 2 apples and 6 oranges, and a blue box with 3 apples and 1 orange. The probability of selecting a red box and blue box is 40% and 60% respectively.

Considering the following chart:

```
apple  |  2  |  3  |

orange |  6  |  1  |

        red    blue

P(apple| red)=count(apples in red)/count(apples and oranges in red) = 1/4
P(apple|blue)=count(apples in blue)/count(apples and oranges in blue)=3/4
P(orange|red)=count(oranges in red)/count(apples and oranges in red)=3/4
P(orange|blue)=count(oranges in blue)/count(apples and oranges in blue)=1/4

```

Now, I know it's wrong but intuitively why is it wrong to calculate:

```
P(red|apple)=count(apples in red)/count(all the apples)=2/5
P(blue|apple)=count(apples in blue)/count(all the apples)=3/5
P(red|orange)= count(oranges in red)/count(all the oranges)=6/7
P(blue|orange)= count(oranges in blue)/count(all the oranges)=1/7

```

but we rather apply Bayes theorem to calculate the above conditional probabilities, like

```
P(red|orange)=P(orange|red)*P(red)/P(orange)=3/4*4/10*20/9=2/3

```

How do I identify that Bayes Theorem is the right way to calculate the probabilities for a certain problem and using the counts will put me on the wrong way. What's the intuition behind it?

Thanks!