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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.

1. What is the probability of drawing a card with an addition or subtraction problem on it?

2. If Mr. Hill adds $40$ division flashcards to the deck, what will P(division) be?

3. 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.

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

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

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?

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

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

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

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

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?

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