### Probability Problems – ACT Math

Probability problems on the ACT math test will ask you about the chance of something happening.

You can calculate probability by using a ratio or percentage.

Have a look at these examples:

**Problem 1:**

A radio station offers free competitions. Normally, one in every twenty contestants wins the free competition. What is the probability of losing the free competition?

A. 1/20

B. 1/19

C. 19/20

D. 19/1

E. 20/19

** The correct answer is C.**

The probability of success is represented by a fraction, with the chance of success in the numerator and the total amount in the denominator.

^{1}/_{20}

The chance of losing can therefore be calculated by subtracting the fraction for the chance of winning from the fraction representing the total.

^{20}/_{20} – ^{1}/_{20} = ^{19}/_{20}

Note that fractions are slightly different than ratios.

^{1}/_{20} = 1 in 20 (so there are 20 parts in total)

On the other hand, a ratio is expressed as follows:

1: 34 = 1 to 34

In other words, there are 35 parts in total in the above example.

**Problem 2:**

An owner of a carnival attraction draws teddy bears out of a bag at random to give to prize winners. She has 10 brown teddy bears, 8 white teddy bears, 4 black teddy bears, and 2 pink teddy bears when she opens the attraction at the start of the day. What is the probability that the first prize winner of the day will receive a pink teddy bear?

A. ^{1}/_{24}

B. ^{2}/_{24}

C. ^{1}/_{2}

D. ^{1}/_{22}

E. ^{2}/_{22}

**The correct answer is B.**

This is a question on calculating basic probability.

Calculate how many items there are in total in the data set, which is also called the “sample space” or (*S*).

The owner has 10 brown teddy bears, 8 white teddy bears, 4 black teddy bears, and 2 pink teddy bears when she opens the attraction at the start of the day.

So, at the start of the day, she has 24 teddy bears: 10 + 8 + 4 + 2 = 24

The event is the chance of the selection of a pink teddy bear. We know that there are two pink teddy bears at the start of the day.

Finally, we need to put the event (the number representing the chance of the desired outcome) in the numerator and the number of possible remaining combinations (the sample space) in the denominator.

So the answer is ^{2}/_{24}.