Introduction to Basic Probability Word Problems
Life is a school of probability.
—WALTER BAGEHOT (1826–1877)
This lesson will cover the basics of probability and will show you how to apply these concepts to word problems.
Simple Probability
The probability of a certain event can be found by using the formula:
To find the total number of possible outcomes, make a list of the possibilities. This list is called a sample space. For example, when you are flipping a coin, the sample space is {heads, tails} and when you are rolling a number cube, the sample space is {1, 2, 3, 4, 5, 6}.
Now, let's practice finding the probability of some simple events. For example, when you are flipping a coin, there are two sides and one of the sides is heads. Therefore, the probability of getting heads when flipping a coin is .
When you are rolling a number cube, there are six sides and one of them has a 4 on it. Therefore, the probability of rolling a number cube and getting a 4 is .
Tip:It is common to encounter probability questions about playing cards. There are 52 cards in a standard deck; 26 of these are red and 26 are black. There are 13 cards in each of the four suits of cards: diamonds (red), hearts (red), clubs (black), and spades (black). There are three face cards in each suit; the jack, the queen, and the king are each considered a face card. |
Use the steps to solving word problems to solve the following simple probability question:
What is the probability of selecting a black card at random from a standard deck of 52 cards?
Read and understand the question. This question is looking for the probability of selecting one black card from a standard deck. There are 52 cards in a standard deck.
Make a plan. Use the fact that there are 52 cards in the deck and the fact that 26 of those cards are black. Substitute into the formula
Carry out the plan. The formula becomes P(black card) . The probability is equal to .
Check your answer. To check this answer, substitute the values again to see if the answer is reasonable. Since 26 out of the 52 cards of the deck are black, half of the cards are black. Thus, the probability is equal to . This answer is checking.
Tip:The probability of an impossible event is equal to 0. The probability of an event certain to happen is equal to 1. The probability of any other event is always a value between 0 and 1. |
Finding the Probability That an Event will not Happen
The probability of an event not happening is always equal to the probability of the event happening subtracted from one. The formula is P(not E) = 1 – P(E). For example, if the probability of selecting a heart from a standard deck of cards is , then the probability of not selecting a heart is .
Compound Probability ("or" Statements)
When you are finding the probability of events with two or more conditions, add the probabilities together. For example, to find the probability of rolling a 2 or a 3 when you are rolling a number cube, the probability of rolling a 2 is and the probability of rolling a 3 is . Thus, the probability of rolling a 2 or a 3 is P(2 or 3) . Because these two events could not occur at the same time, these are known as mutually exclusive events.
Tip:In probability questions, the key word or tells you to add the probabilities together. |
What about events that are not mutually exclusive? Take, for example, the event of rolling a number cube. What is the probability that you roll a 4 or an even number? This time, rolling a 4 satisfies the first condition and rolling a 2, 4, or 6 satisfies the second condition. Because rolling a 4 satisfies both conditions, these events are not mutually exclusive. Therefore, to find the probability of rolling a 4 or an even, count the number of ways each event can happen and subtract the number of ways that both conditions are satisfied. The probability of rolling a 4 or an even number is equal to .
Find practice problems and solutions for these concepts at Basic Probability Word Problems: Practice Questions.
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