Tip #36 to Get a Top ACT Math Score

They don't take the ACT over there in England, but Scary, Baby, Ginger, Posh, and Sporty summed up probability in 1996. Like functions, probability could be the topic of a college course, but the ACT asks only one thing! To find out about that one thing, please get out your credit card and see my website.

I'm kidding. The one thing is:    

In English that's "probability equals what you want, divided by the total number of things you are choosing from." Thanks again to Scary, Baby, and the gang.

Let's look at this question:

Solution: Anytime you see the word "probability," use the equation

We want anything but solid pink socks, so there are 14 we'd be happy with, and that number goes on top. The total number of socks to choose from is 18, so that number goes on bottom. So the probability of not selecting a solid pink sock is .

Correct answer: K

Probability in school could be much harder than that, but it's NEVER harder on the ACT. is all they ask!

Example Problems

Easy

1. If 8 out of 12 marbles in a bag are green, what is the probability that a marble selected at random from the bag will NOT be green?
   1. 
   2. 
   3. 
   4. 
   5. 1

Medium

2. A bag contains 30 marbles, all solid-colored. Each marble is blue, red, or yellow. If the probability of choosing a blue marble is and the probability of choosing a red marble is , how many yellow marbles are in the bag?
   6. 5
   7. 6
   8. 7
   10. 8
   11. 9
3. The triangle shown below is used at a carnival. People try to toss a penny onto the shaded region to win a prize. If the area of the whole figure is 12 and the area of the unshaded triangle is 7.5, what is the probability of randomly tossing a penny onto the shaded region?



1. 4.5
2. 1
3. 
4. 

5. 

Answers

1. B Probability so the probability of NOT selecting a green marble is This question requires that we reduce the No problem. Stop looking at me like that, reducing is easy, just divide the top and bottom of the fraction by the same number. Or, if you really don't like reducing, just use your calculator. Divide 4 by 12 to get 0.333. Then divide each answer choice (top by the bottom) to get decimals and see which one matches 0.333. Nice.
2. F There are 30 marbles total. are blue. So times the total number of marbles equals the amount of blue marbles. ()(30) = 20, so there are 20 blue marbles. are red, and ()(30) = 5, so there are 5 red marbles. The rest are yellow. So 30 – 20 – 5 = 5, and there are 5 yellow marbles.
3. D Probability We want to land in the shaded region. The area of the shaded region where we want to land is: total area – unshaded = shaded, or 12 – 7.5 = 4.5. Great review of Donuts (Skill 20, Area shaded equals area big guy minus area donut hole.) The total area of the figure is given as 12. So the probability of landing in the shaded region is Oddly, that does not match any answers. Do we freak out; do we assume we're wrong? No! See if any of the answers are equivalent to our answer, by either looking at the fractions or just turning them into decimals on your calculator. Choice D is correct since

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