1.1. Independent Events http://www.ck12.org
1.1 Independent Events
Learning Objectives
- Know the definition of the notion of independent events.
- Use the rules for addition, multiplication, and complementation to solve for probabilities of particular events
in finite sample spaces.
What is Probability?
The simplest definition of probability is the likelihood of an event. If, for example, you were asked what the
probability is that the sun will rise in the east, your likely response would be 100%. We all know that the sun rises in
the east and sets in the west. Therefore, the likelihood that the sun will rise in the east is 100% (or all the time). If,
however, you were asked the likelihood that you were going to eat carrots for lunch, the probability of this happening
is not as easy to answer.
Sometimes probabilities can be calculated or even logically deduced. For example, if you were to flip a coin, you
have a^5050 chance of landing on heads so the probability of getting heads is 50%. The likelihood of landing on heads
(rather than tails) is 50% or^12. This is easily figured out more so than the probability of eating carrots at lunch.
Probability and Weather Forecasting
Meteorologists use probability to determine the weather. In Manhattan on a day in February, the probability of
precipitation (P.O.P.) was projected to be 0.30 or 30%. When meteorologists say the P.O.P. is 0.30 or 30%, they are
saying that there is a 30% chance that somewhere in your area there will be snow (in cold weather) or rain (in warm
weather) or a mixture of both. If you were planning on going to the beach and the P.O.P. was 0.75, would you go?
Would you go if the P.O.P. was 0.25?
However, probability isn’t just used for weather forecasting. We use it everywhere. When you roll a die you can
calculate the probability of rolling a six (or a three), when you draw a card from a deck of cards, you can calculate
the probability of drawing a spade (or a face card), when you play the lottery, when you read market studies they
quote probabilities. Yes, probabilities affect us in many ways.
Bias and Probability
A. Eric Hawkins is taking science, math, and English, this semester. There are 30 people in each of his classes. Of
these 30 people, 25 passed the science mid-semester test, 24 passed the mid-semester math test, and 28 passed the
mid-semester English test. He found out that 4 students passed both math and science tests. Eric found out he passed
all three tests.
(a) Draw a VENN DIAGRAM to represent the students who passed and failed each test.
(b) If a student’s chance of passing math is 70%, and passing science is 60%, and passing both is 40%, what is the
probability that a student, chosen at random, will pass math or science.
At the end of the lesson, you should be able to answer this question. Let’s begin.
Probability and Odds
The probability of something occurring is not the same as the odds of an event occurring. Look at the two formulas
below.