15 10probability

Information about 15 10probability

Published on January 14, 2008

Author: Dario

Source: authorstream.com

Content

15.10 Probability:  15.10 Probability The probability of an outcome for a particular event is a number telling us how likely a particular outcome is to occur. This number is the ratio of the number of ways the outcome may occur to the number of total possible outcomes for the event. Probability is usually expressed as a fraction, decimal, or percent. Since the number of ways a certain outcome may occur is always smaller or equal to the total number of outcomes, the probability of an event is some number from 0 through 1. :  The probability of an outcome for a particular event is a number telling us how likely a particular outcome is to occur. This number is the ratio of the number of ways the outcome may occur to the number of total possible outcomes for the event. Probability is usually expressed as a fraction, decimal, or percent. Since the number of ways a certain outcome may occur is always smaller or equal to the total number of outcomes, the probability of an event is some number from 0 through 1. What is an event? An event is an experiment or collection of experiments. Examples: The following are examples of events. 1) A coin toss.(2) Rolling a die. (3) Rolling 5 dice. 4) Drawing a card from a deck of cards. 5) Drawing 3 cards from a deck. 6) Drawing a marble from a bag of different colored marbles. 7) Spinning a spinner in a board game. :  What is an event? An event is an experiment or collection of experiments. Examples: The following are examples of events. 1) A coin toss.(2) Rolling a die. (3) Rolling 5 dice. 4) Drawing a card from a deck of cards. 5) Drawing 3 cards from a deck. 6) Drawing a marble from a bag of different colored marbles. 7) Spinning a spinner in a board game. Possible Outcomes of an Event Possible outcomes of an event, also called the sample space, are the results which may occur from any event. :  Possible Outcomes of an Event Possible outcomes of an event, also called the sample space, are the results which may occur from any event. The following are possible outcomes (sample space) of events. :  The following are possible outcomes (sample space) of events. 1) A coin toss has two possible outcomes. The outcomes (sample space) are "heads" and "tails". 2) Rolling a regular six-sided die has six possible outcomes. You may get a side with 1, 2, 3, 4, 5, or 6 dots. 3) Drawing a card from a regular deck of 52 playing cards has 52 possible outcomes. Each of the 52 playing cards is different, so there are 52 possible outcomes for drawing a card. Suppose there are 10 balls in a bucket numbered as follows: 1, 1, 2, 3, 4, 4, 4, 5, 6, and 6. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball numbered 1? There are 2 ways to draw a 1, since there are two balls numbered 1. The total possible number of outcomes is 10, since there are 10 balls. The probability of drawing a 1 is the ratio 2/10 = 1/5. :  Suppose there are 10 balls in a bucket numbered as follows: 1, 1, 2, 3, 4, 4, 4, 5, 6, and 6. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball numbered 1? There are 2 ways to draw a 1, since there are two balls numbered 1. The total possible number of outcomes is 10, since there are 10 balls. The probability of drawing a 1 is the ratio 2/10 = 1/5. Suppose there are 10 balls in a bucket numbered as follows: 1, 1, 2, 3, 4, 4, 4, 5, 6, and 6. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball with a number greater than 4? There are 3 ways this may happen, since 3 of the balls are numbered greater than 4. The total possible number of outcomes is 10, since there are 10 balls. The probability of drawing a number greater than 4 is the ratio 3/10. Since this ratio is larger than the one in the previous example, we say that this event has a greater chance of occurring than drawing a 1. :  Suppose there are 10 balls in a bucket numbered as follows: 1, 1, 2, 3, 4, 4, 4, 5, 6, and 6. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball with a number greater than 4? There are 3 ways this may happen, since 3 of the balls are numbered greater than 4. The total possible number of outcomes is 10, since there are 10 balls. The probability of drawing a number greater than 4 is the ratio 3/10. Since this ratio is larger than the one in the previous example, we say that this event has a greater chance of occurring than drawing a 1. Suppose there are 10 balls in a bucket numbered as follows: 1, 1, 2, 3, 4, 4, 4, 5, 6, and 6. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball with a number greater than 6? Since none of the balls are numbered greater than 6, this can occur in 0 ways. The total possible number of outcomes is 10, since there are 10 balls. The probability of drawing a number greater than 6 is the ratio 0/10 = 0. :  Suppose there are 10 balls in a bucket numbered as follows: 1, 1, 2, 3, 4, 4, 4, 5, 6, and 6. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball with a number greater than 6? Since none of the balls are numbered greater than 6, this can occur in 0 ways. The total possible number of outcomes is 10, since there are 10 balls. The probability of drawing a number greater than 6 is the ratio 0/10 = 0. Suppose there are 10 balls in a bucket numbered as follows: 1, 1, 2, 3, 4, 4, 4, 5, 6, and 6. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball with a number less than 7? Since all of the balls are numbered less than 7, this can occur in 10 ways. The total possible number of outcomes is 10, since there are 10 balls. The probability of drawing a number less than 7 is the ratio 10/10 = 1. Note in the last two examples that a probability of 0 meant that the event would not occur, and a probability of 1 meant the event definitely would occur. :  Suppose there are 10 balls in a bucket numbered as follows: 1, 1, 2, 3, 4, 4, 4, 5, 6, and 6. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball with a number less than 7? Since all of the balls are numbered less than 7, this can occur in 10 ways. The total possible number of outcomes is 10, since there are 10 balls. The probability of drawing a number less than 7 is the ratio 10/10 = 1. Note in the last two examples that a probability of 0 meant that the event would not occur, and a probability of 1 meant the event definitely would occur. Suppose a card is drawn at random from a regular deck of 52 cards. What is the probability that the card is an ace? There are 4 different ways that the card can be an ace, since 4 of the 52 cards are aces. There are 52 different total outcomes, one for each card in the deck. The probability of drawing an ace is the ratio 4/52 = 1/13. :  Suppose a card is drawn at random from a regular deck of 52 cards. What is the probability that the card is an ace? There are 4 different ways that the card can be an ace, since 4 of the 52 cards are aces. There are 52 different total outcomes, one for each card in the deck. The probability of drawing an ace is the ratio 4/52 = 1/13. Suppose a card is drawn at random from a regular deck of 52 cards. What is the probability that the card is a face card?:  Suppose a card is drawn at random from a regular deck of 52 cards. What is the probability that the card is a face card? Suppose a card is drawn at random from a regular deck of 52 cards. What is the probability that the card is a “one-eyed jack”?:  Suppose a card is drawn at random from a regular deck of 52 cards. What is the probability that the card is a “one-eyed jack”? Suppose a card is drawn at random from a regular deck of 52 cards. What is the probability that the card is red?:  Suppose a card is drawn at random from a regular deck of 52 cards. What is the probability that the card is red? Suppose a regular die is rolled. What is the probability of getting a 3 or a 6? There are a total of 6 possible outcomes. Rolling a 3 or a 6 are two of them, so the probability is the ratio of 2/6 = 1/3. :  Suppose a regular die is rolled. What is the probability of getting a 3 or a 6? There are a total of 6 possible outcomes. Rolling a 3 or a 6 are two of them, so the probability is the ratio of 2/6 = 1/3. A class has 13 male and 15 female students. If a student is randomly selected, what is the probability the student is a male?:  A class has 13 male and 15 female students. If a student is randomly selected, what is the probability the student is a male?

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