Probability questions on the math part of the test will involve calculating probability in order to make predictions.
What is Probability?
Students sometimes ask: What is probability?
First of all, remember that probability can be expressed as a fraction or as a percentage.
For instance, something that has a 1 in 10 chance of happening can be expressed as a probability of 1/10 or as a 10% probability.
Probability − The Basic Concepts
In order to determine probability, you need two concepts: subset and data set.
The subset is the group of items from which you are hoping to select your item.
So, for example, if the problem tells you that you have cards with hearts, spades, diamonds, and clubs, and you want to draw clubs, then clubs is your subset.
The total amount of cards in the deck is your data set.
For probability equations, the amount of items in the subset needs to go in the numerator of your fraction, while the amount of total items remaining in the data set needs to go in the denominator of your fraction.
Now try the problems on probability that follow.
Probability − Drawing from a Single Subset
(1) Use the information below to answer the probability problem that follows.
- The owner of a store gives away candy of different colors to its customers.
- The store owner draws the candy from a bag at random without looking at it before giving it to the customer.
- There are 75 pieces of candy available in total when the store opens.
- 20 pieces of the candy are red, 15 are orange, 23 are green, and 17 are purple.
If the first piece of candy she gives away is purple, what is the probability that the next piece of candy she draws from the bag will be orange?
A. 14/74
B. 15/74
C. 14/75
D. 15/75
E. 16/75
For questions on probability like this one, you need to reduce the quantity of the total data set by the quantity of items already drawn.
STEP 1: Determine the total amount in the data set after any items have been removed.
There are 75 pieces of candy in total before any are drawn.
Then 1 piece of candy is removed.
75 − 1 = 74
STEP 2: Determine the amount in the subset.
The first piece of candy is purple, so we would need to reduce the subset for that particular color by 1.
However, the question is asking us about the probability that the second piece of candy will be orange, not purple.
There are 15 pieces of orange candy, and a piece of orange candy has not been drawn so far.
STEP 4: The probability is expressed as a fraction.
The amount in the subset (15 pieces of orange candy) goes on the top of the fraction and the amount of items left in the data set (74 pieces of candy left) goes on the bottom.
Therefore, the answer is 15/74.
So, the correct answer is B.
Probability − Drawing from Multiple Subsets
(2) Use the information below to answer the probability problem that follows.
- An owner of a stall at a carnival gives away stuffed animals as prizes.
- He takes the stuffed animals from a barrel at random without looking at them before giving them to the prize winners.
- He has 15 stuffed teddy bears, 12 stuffed rabbits, 5 stuffed monkeys, 8 stuffed unicorns, and 10 stuffed dinosaurs in the barrel when he opens the stall.
If the first animal he gives away is a rabbit and the second is a monkey, what is the probability that the next animal will be a unicorn or a dinosaur?
A. 18/48
B. 18/50
C. 8/48
D. 10/48
E. 16/48
STEP 1: Your first step is to determine the number of items in the data set, before any items are removed.
Here, we have 15 stuffed teddy bears, 12 stuffed rabbits, 5 stuffed monkeys, 8 stuffed unicorns, and 10 stuffed dinosaurs in the barrel when he opens the stall.
15 + 12 + 5 + 8 + 10 = 50
STEP 2: Determine the amount in the data set after any items have been removed.
We know that the first animal he gives away is a rabbit and the second is a monkey, so he has taken two items from the data set.
50 – 2 = 48
STEP 3: Determine the amount in the subset.
Our subset is unicorns or dinosaurs. No unicorns or dinosaurs have been used so far.
8 + 10 = 18 unicorns or dinosaurs remaining
STEP 4: The probability is expressed as a fraction, with the subset on the top and the data set on the bottom.
18/48
So, the correct answer is A.