12.7. Basic Probability http://www.ck12.org
20 · 0. 30 · 0. 1 = 0. 006 = 0 .6%
The naïve approach would be to simply add the three probabilities together. This is incorrect. The better way to
approach the problem is to ask the question: what is the probability that none of the events occur?
8 · 0. 7 · 0. 9 = 0. 504
The probability that at least one occurs is the complement of none occurring.
1 − 0. 504 = 0. 496 = 49 .6%
Practice
A card is chosen from a standard deck.
- What’s the probability that the card is a queen?
- What’s the probability that the card is a queen or a spade?
You toss a nickel, a penny, and a dime. - List all the possible outcomes (the elements in the sample space).
- What is the probability that the nickel comes up heads?
- What is the probability that none of the coins comes up heads?
- What is the probability that at least one of the coins comes up heads?
A bag contains 7 red marbles, 9 blue marbles, and 10 green marbles. You reach in the bag and choose 4 marbles,
one after the other, without replacement. - What is the probability that all 4 marbles are red?
- What is the probability that you get a red marble, then a blue marble, then 2 green marbles?
You take a 40 question multiple choice test and believe that for each question you have a 55% chance of getting it
right. - What is the probability that you get all the questions right?
- What is the probability that you get all of the questions wrong?
A player rolls a pair of standard dice. Find each probability.
11.P(sum is even)
12.P(sum is 7 )
13.P(sum is at least 3 ) - You want to construct a 3 digit number at random from the digits 4, 6, 8, 9 without repeating digits. What is the
probability that you construct the number 684? - In poker, a straight is 5 cards in a row (ex. 3, 4, 5, 6, 7), NOT all the same suit (if they are all the same suit it
is considered a straight flush or a royal flush). A straight can start or end with an Ace. What’s the probability of a
straight?For an even bigger challenge, see if you can calculate the probabilities for all of the poker hands.