We think it's highly likely that you've already dealt with probability today. Did you see the weather forecast? Is there a 30% chance of rain? Did you decide not to study for your foreign language class since you had a pop quiz yesterday? All of these predictions and decisions are based on probability and statistics.
Probability is related to statistics because most probabilities are based on statistics of past events. That's why we usually study statistics first. To understand probability, it is important to know where the data comes from.
Probabilities are simply fractions that can also be written as percents or ratios. The numerator of a probability is the number of outcomes that satisfy the condition of the probability. The denominator is the total number of possible outcomes.
What is the probability that the sum of two six-sided dice will be greater than 10?
First we need to look at all of the possible sums we can get from rolling two dice. Each die has these possible outcomes: 1, 2, 3, 4, 5, and 6. We can make a table to represent the combinations.
As you can see there are 36 possible combinations, 3 of which are greater than 10, and these are shaded. So, we have 36 possible outcomes and 3 favorable ones:
First, it's important to know what is in a deck of cards
|52 cards (not including Jokers)|
|26 red and 26 black|
|4 suits: diamonds, clubs, hearts, and spades|
|clubs and spades are black|
|diamonds and hearts are red|
|13 cards in each suit: A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K|
|3 face cards in each suit: Jack, Queen, King|
If you draw a card from a standard deck of cards, what is the probability of drawing a face card?
There are 4 suits with 3 face cards each. This makes a total of 3 × 4 = 12 face cards out of 52 cards.
If you draw a card from a standard deck of cards, what is the probability of not drawing a spade?
There are 13 spades, so that means that there are 52 – 13 = 39 cards that are not spades.
If you roll two dice, what is the probability that the sum of the two is odd?
As we can see in the chart above, there are 18 combinations that result in an odd sum. There are still 36 different combinations, so:
What is the probability of flipping a coin and not landing on heads?
What is the probability of rolling a die and not getting a 1?
What is the probability of drawing a number card less than 4 from a standard deck of cards?