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Notes on PROBABILITY

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What is Probability? Probability is a number from 0 to 1 that tells you how likely something is to happen. Probability can be either theoretical or experimental. If you flip a coin, the probability it will land on heads is ½. P(heads)

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A new baby will be boy girl If you toss a coin it will land Heads up Tails up

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The probability of the baby being a boy is … impossible certain 50 - 50 01½ 1 in 2½ The probability of a coin landing heads up is also 50 – 50, 1 in 2, or ½.

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The probability number line Impossible events have a probability of 0 impossible certain 50 - 50 01½ Events that are certain are given a probability of 1

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Like all number lines we can mark other points on it. 01½¼¾ If I pick a card at random from a stack of 4 cards that are numbered 1, 2, 3, 4, the probability that it will be a three is…? Can you work out why?

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01½¼¾ If I pick a card at random from that same pack of cards, the probability that it will be an even number is…? Can you work out why?

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Probability THEORETICAL Theoretical probability can be found without doing an experiment. It is what is supposed to happen. EXPERIMENTAL Experimental probability is found by repeating an experiment and observing the outcomes.

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THEORETICAL PROBABILITY I have a quarter. My quarter has a heads side and a tails side. Since my quarter has only 2 sides, there are only 2 possible outcomes when I flip it. It will either land on heads, or tails. HEADS TAILS

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THEORETICAL PROBABILITY When I flip my coin, the probability that my coin will land on heads is 1 in 2. What is the probability that my coin will land on tails? HEADS TAILS

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Theoretical Probability Right!!! There is a 1 in 2 probability that my coin will land on tails!!! HEADS TAILS A probability of 1 in 2 can be written in three ways: As a fraction: ½ As a decimal:.50 As a percent: 50%

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Theoretical probability When I spin this spinner, I have a 1 in 4 chance of landing on the section with the red A in it. A A A A

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A 1 in 4 chance can be written 3 ways: As a fraction: ¼ As a decimal:.25 As a percent: 25% A A A A Theoretical Probability

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Other examples of theoretical probability are found in determining the probability of drawing a certain card from a standard deck of cards. A standard deck has four suits: spades ( ), hearts ( ), diamonds ( ), and clubs ( ). It has thirteen cards in each suit: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Each of these cards is equally likely to be drawn.

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The probability of drawing a king is given by: The probability of drawing a heart is given by:

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The probability of drawing a face card (jack, queen, king) is given by:

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Dice (singular is die) are cubes that have spots on each side. The spots are usually numbered from 1 to 6. When a fair die is tossed, each side has an equally likely chance of ending up on top. The probability of tossing a die and having a 4 end up on top (this is called rolling a 4) is given by:

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The probability of tossing a die and rolling a 7 is given by: The probability of tossing a die and rolling a number less than 7 is given by:

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These examples lead to four rules or facts about probability: 1. The probability of an event that cannot occur is 0. 2. The probability of an event that must occur is 1. 3. Every probability is a number between 0 and 1 inclusive. 4. The sum of the probabilities of all possible outcomes of an experiment is 1.

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I am going to take 1 marble from the bag. What is the probability that I will pick out a red marble? Theoretical Probability I have three marbles in a bag. 1 marble is red. 1 marble is blue. 1 marble is green.

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Theoretical Probability Since there are three marbles and only one is red, I have a 1 in 3 chance of picking out a red marble. I can write this in three ways: As a fraction: 1/3 As a decimal:.33 As a percent: 33%

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Experimental Probability Experimental probability is found by repeating an experiment and observing the outcomes.

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Remember the bag of marbles? The bag has only 1 red, 1 green, and 1 blue marble in it. There are a total of 3 marbles in the bag. Theoretical Probability says there is a 1 in 3 chance of selecting a red, a green or a blue marble.

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Experimental Probability Draw 1 marble from the bag. It is a red marble. Record the outcome on the tally sheet

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Experimental Probability Put the red marble back in the bag and draw again. This time your drew a green marble. Record this outcome on the tally sheet.

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Experimental Probability Place the green marble back in the bag. Continue drawing marbles and recording outcomes until you have drawn 6 times. (remember to place each marble back in the bag before drawing again.) blue, green, red, green

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Experimental Probability After 6 draws your chart will look similar to this. Look at the red column. Of our 6 draws, we selected a red marble 2 times.

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Experimental Probability The experimental probability of drawing a red marble was 2 in 6. This can be expressed as a fraction: 2/6 or 1/3 a decimal :.33 or a percentage: 33%

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Experimental Probability Notice the Experimental Probability of drawing a red, blue or green marble.

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Comparing Experimental and Theoretical Probability Look at the chart at the right. Is the experimental probability always the same as the theoretical probability?

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Comparing Experimental and Theoretical Probability In this experiment, the experimental and theoretical probabilities of selecting a red marble are equal.

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Comparing Experimental and Theoretical Probability The experimental probability of selecting a blue marble is less than the theoretical probability. The experimental probability of selecting a green marble is greater than the theoretical probability. The more you do an experiment, the closer you get to the theoretical probability.

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Probability Review Theoretical (what is supposed to happen, can be found without doing an experiment) Experimental (can be found by repeating an experiment and recording outcomes.) There are 2 types of probability: Probability is a number from 0 to 1 that tells you how likely something is to happen.

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Probability Review Probability can be expressed as a fraction, a decimal or a percentage.

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