There are a number of assumptions in the given scenario -
The first assumption is that the player is using a $60$ card deck. The deck contains a ratio of $24:60$ lands so $24$ lands total.
They are the second player who draws a card on their first turn.
Of the given lands, there is $6$ mountains(which produce red mana),$10$ forests(which produce green mana) and $8$ sources that can generate both colors(both red and green mana).
Assuming the player has drawn a starting hand of $7$ cards. The hand contains $3$ lands $= 3$ cards that can produce mana. The hand contains one of each type of mana generator($1$ mountain, $1$ forest, $1$ that produces both).
What are the chances that this players next draw will be:
1). Any mana producing source?
2). A green mana producing source? (including sources that can produce both)
3). A red mana Producing source? (including sources that can produce both)
4). A source that generates both mana types?
After the hand has been drawn, there is a new ratio of $21:53$ lands to cards in the deck.
Of those $21$ lands, $16$ create green, $12$ create red(The red and green totals include the $7$ that create both), and $7$ create both.
Using this info the chances of the four questions are as follows -
1). $21/53 = 39.6226$ %
2). $16/53 = 30.1886$ %
3). $12/53 = 22.6415$ %
4). $ 7/53 = 13.2075$ %