CPM Homework Help : MC2 Problem 3-23

Mr. Hill has a deck of math flashcards that include addition, subtraction, and multiplication problems. Twenty-five cards show addition problems, $30$ are subtraction problems, and $45$ are multiplication problems.

What is the probability of drawing a card with an addition or subtraction problem on it?
If Mr. Hill adds $40$ division flashcards to the deck, what will P(division) be?
In the new deck, which is greater: the probability of drawing an addition or subtraction flashcard, or the probability of drawing a multiplication or division flashcard? Justify your conclusion.

Hint (a):

$\text{P(additional problem) }= \frac{25}{100}$

$\text{P(subtraction problem) }= \frac{30}{100}$

Help (a):

Since you know how to get the probability of drawing an addition or a subtraction problem separately, how could you get the probability of drawing either an addition or subtraction problem in one draw?

More Help (a):

Try adding the separate probabilities together. Does this make sense? Why?

Help (b):

If the $40$ division flashcards are added, how many division problems would there be in the deck?

More Help (b):

How many total cards are in the deck now?
Remember, $40$ cards were just added so the total amount of cards is larger.

Answer (b):

$\frac{40}{140} = \frac{2}{7}$

Help (c):

Out of the new deck with the $40$ added division cards, is it more likely to draw either an addition or subtraction card or to draw either a multiplication or division card?

Answer (c):

Drawing a multiplication or division card is more likely. Why is this the answer?