Lesson 0 -11 Simple Probability and Odds

The probability of an event is the ratio of the number of favorable outcomes for the event to the total number of possible outcomes. The list of all possible outcomes is called the sample space. What is the probability of rolling a number bigger than 4 on a dice? Favorable outcomes: 5 or 6 Number of favorable outcomes: 2 Possible outcomes: 1, 2, 3, 4, 5, or 6 Number of possible outcomes: 6 There is a 1 in 3 probability of rolling a number bigger than 4.

The spinner at the right is spun. Example 1 Probability The spinner at the right is spun. a. Find the probability of spinning an A or C. There are five possible outcomes. There are two favorable outcomes, A and C. probability = So, P(A or C) = b. Find the probability of spinning a consonant. Three of the five outcomes are consonants: B, C, and D. So, there are three favorable outcomes. probability = So, P(consonant) =

Example 2 Probability A box contains 8 yellow marbles, 4 green marbles, 1 red marble, and 11 blue marbles. One marble is randomly drawn. Find each probability. a. green There are 4 green marbles and 24 total marbles.  number of favorable outcomes  number of possible outcomes P(green marble) = The probability can be stated as , about 0.17, or about 17%. b. red or blue There are 1 + 11 or 12 marbles that are red or blue. P(red or blue) = The probability can be stated as , 0.5, or 50%.

Example 2 Probability A box contains 8 yellow marbles, 4 green marbles, 1 red marble, and 11 blue marbles. One marble is randomly drawn. Find each probability. c. not yellow “Not yellow” is the complement of “yellow”. There are 4 + 1 + 11 or 16 marbles that are not yellow. P(not yellow) = = or about 0.67 The probability can be stated as , about 0.67, or about 67%.

A compound event consists of two or more simple events. Anything can be a simple event: Flipping a coin. Rolling a die. Picking a card. A football game. A down in a football game. An inning in a baseball game. An out in a baseball game. Putting on your shoes. Picking your nose.

Independent and dependent events If the second event is not influenced by the first event then it is an independent event. Example: 1st event – flip a coin. 2nd event – roll a die. The first event does not effect the probability of a particular outcome of the second event. Thus they are independent.

Independent and dependent events If the second event is influenced by the first event then it is a dependent event. Example: 1st event – You pick someone to be on your team. 2nd event – The other captain picks someone to be on his team. The first event changes the probability of a particular outcome of the second event. Thus the 2nd event is dependent on the outcome of the 1st event. The same player can’t be picked by both team captains.

Probability tree A restaurant lunch special includes a choice of soup: chicken noodle, tortilla, tomato, and French onion and a choice of salad: house or Caesar. Use a tree diagram to determine the number of different lunch specials possible. 1st event: Pick the soup. 2nd event: Pick the salad Outcomes Chicken noodle, house house Chicken noodle Caesar Chicken noodle, Caesar house tortilla, house Tortilla Caesar tortilla, Caesar house tomato, house Tomato Caesar tomato, Caesar house French onion, house French onion Caesar French onion, Caesar The tree diagram shows that there are 8 possible outcomes.

number of choices of sweatshirts Example 4 Fundamental Counting Principle a. Students can order school sweatshirts in four different colors, two different styles, and five different sizes. Use the Fundamental Counting Principle to determine the number of choices possible. We can use the Fundamental Counting Principle to find the number of possible choices. number of styles number of colors number of sizes number of choices of sweatshirts So, there are 40 different choices of sweatshirts.

Example 4 Fundamental Counting Principle b. There are 8 students remaining in the spelling bee. How many possible ways are there to award first, second, and third place? We can use the Fundamental Counting Principle to find the number of possible ways to award first, second, and third place. number of 2nd place choices Number of 1st place choices number of 3rd place choices number of ways to award 1st thru 3rd So, there are 336 possible ways to award first, second, and third place.

So, the odds of choosing a purple chip are or 3:7. Example 5 Odds A bag contains 5 yellow chips, 2 blue chips, and 3 purple chips. If one chip is randomly chosen, find the odds of choosing a purple chip. Odds is a ratio of the number of possible successes to the number of possible failures. There are ten possible outcomes; 3 are successes and 7 are failures. So, the odds of choosing a purple chip are or 3:7.