Probability

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

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


The number of possible ways something can happen

or

Probabilities range from zero (it’s impossible) to 1 (it’s certainly going to happen). Probabilities are usually expressed as fractions but you might see them expressed as a decimal or a percent.  All the probabilities of how something can happen must add up to one. For example, the probabilities of heads and tails when flipping a coin are each 1/2.  When you add them together, the sum is 1.  That means you’ve accounted for all the ways something can turn out–certainty–a probability of 1.

More words of “Wiz-dom” on Probability #1

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

More words of “Wiz-dom” on Probability #2

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 #1

Words of “Wiz-dom” Sometimes the test writer wants to know the probability of “independent” events occurring simultaneously. All you need to do is determine the probability of each event and then multiply them together. For example, the probability of an odd number coming up on a green die (1/2) and a “3” coming up on a red die (1/6) at the same time is 1/2 times 1/6 or 1/12.

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 #2

Sample Questions

15.  There are only red, blue and green crystal balls in a bag. The probability of selecting a red one is 1/3 and the probability of selecting a blue one is 2/5. What is the probability of selecting a green one?

(A) 0
(B) 1/4
(C) 4/15
(D) 11/15
(E) 3/4

Answer to Question #15

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

(A) 1/9
(B) 1/7
(C) 1/2
(D) 7/9
(E) 6/7

Answer to Question #5

14.
  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 #14

7.  There are only two roads that go from Gullage to Jaranda. One goes through Harak and the other goes through Igorville. How many possible round trip routes from Gullage to Jaranda and back are there?

(A) 1
(B) 2
(C) 4
(D) 6
(E) 8

Answer to Question #7

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