Probability

Words of “Wiz-dom”—You can count on seeing one or two simple probability problems on the ACT (and on the SAT). They won’t be anything difficult like, “If you skip school tomorrow, what is the probability you’ll get caught?” J

Probability is expressed as a fraction based on the odds something is going to happen. It always reduces to:

The number of desired/correct ways something can happen
DIVIDED BY:
The number of possible ways something can happen

OR:

Probabilities range from zero (it’s impossible) to 1 (it’s certainly going to happen). All the ways something can happen must add up to one. Probabilities are usually expressed as fractions but you might see them expressed as a decimal or a percent.

More words of “Wiz-dom” on Probability

For example, if you flip a coin, the probability of it coming up heads is:

 

More words of “Wiz-dom” on flipping a coin

If you roll a die (the singular of “dice”), the probability of getting an even number is:

You get this answer since there are three even numbers out of the six sides on a die.

What’s the probability of rolling a 3, a number larger than 2, a number evenly divisible by 3?

Answer to rolling a die

Words of “Wiz-dom”— Sometimes the question is simply about how many possible ways some event could happen. Then you need to focus on the number of possible combinations. For example:

There are four flagpoles that each can hold only one flag in the court yard of the Castle of Wizdom. Freelac, my flag tender, chooses four flags from six possible flags to be hung on those poles each day. The Freelac likes to hang the flags in as many different patterns as he can. If he arranges them differently each day, what is the maximum number of days that he can hang the flags before he has to repeat a pattern?

Answer to the maximum number of days

Sample Questions

1. There are only red, blue and green crystal balls in a bag. The probability of selecting a red one is  and the probability of selecting a blue one is . What is the probability of selecting a green one?A. B. C. 

D. 

E. 

Answer to question #1

2.  There are 3 red marbles, 3 green marbles and 3 blue marbles in a bag. The first two marbles drawn from the bag and then thrown away are blue. What is the probability that the next one drawn will be blue?

(A) 
(B) 
(C) 
(D) 

(E) 

Answer to question #2

3.  If Lancelot, my lancer, hits the bull’s-eye with 80% of his throws, what is the probability that he will make two bull’s-eyes on his next two throws?

A. 16%
B. 24%
C. 40%
D. 64%
E. 80%

Answer to question #3

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