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Probability Concepts and Calculations for Beginners

Understand experimental and theoretical probabilities through practical examples. Learn how to calculate probabilities in various scenarios.

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Probability Concepts and Calculations for Beginners

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  1. Probability – 1.6

  2. 1. 2. 1 3. 0.0043 4. 5. 1.04 6. 3 Probability – Warm Up Write each number as a percent. 3 8 5 6 1 400

  3. Probability – Warm Up 1. = 3 ÷ 8 = 0.375 = 0.375(100%) = 37.5% 2. 1 = = 11 ÷ 6 = 1.83 = 1.83(100%) = 183 % 3. 0.0043 = 0.0043(100%) = 0.43% 4. = 1 ÷ 400 = 0.0025 = 0.0025(100%) = 0.25% 5. 1.04 = 1.04(100%) = 104% 6. 3 = 3(100%) = 300% Solutions 3 8 5 6 11 6 1 3 1 400

  4. There are two types of Probability: • Experimental probability – P (event) = number of times the event occurs number of trials • Theoretical Probability – P(A) = m n m = number of favorable outcomes n = number of equally likely outcomes

  5. 8 50 P(bull’s eye) = = 0.16, or 16% Probability A player hit the bull’s eye on a circular dartboard 8 times out of 50. Find the experimental probability that the player hits the bull’s eye.

  6. 2 outcomes result in a multiple of 3. 2 6 6 equally likely outcomes are in the sample space. 1 3 = Probability Find the theoretical probability of rolling a multiple of 3 with a number cube. To roll a multiple of 3 with a number cube, you must roll 3 or 6.

  7. Gene fromMother Bb BBBBb bBbbb Gene fromFather The outcome bb is the only one for which a child will have blue eyes. So, P(blue eyes) = . 1 4 1 4 The theoretical probability that the child will have blue eyes is , or 25%. Probability Brown is a dominant eye color for human beings. If a father and mother each carry a gene for brown eyes and a gene for blue eyes, what is the probability of their having a child with blue eyes? Let B represent the dominant gene for brown eyes. Let b represent the recessive gene for blue eyes. The sample space contains four equally likely outcomes {BB, Bb, Bb, bb}.

  8. Geometry Probability Geometric Probability = area that would give a favorable solution total area Each ring has a width of 1 How do we find the probability of hitting the purple ring? R = 1 Strategy?? In your own words, how would we get the probability of the purple ring

  9. area of outer ring area of circle with radius 4r P(outer ring) = (area of circle with radius 4r) – (area of circle with radius 3r) area of circle with radius 4r = (4r)2 – (3r)2 = (4r2) 16 r2 – 9 r2 = 16 r2 7 r2 = 16 r2 7 16 = 7 16 The theoretical probability of hitting the outer ring is , or about 44%. Probability For the dartboard above, find the probability that a dart that lands at random on the dartboard hits the outer ring. Radius = 1 Each ring has a width of 1

  10. Random Number Generator • When actual trials are difficult to conduct, you can find experimental probabilities by using a simulation, which is the model of one or more events. • To create a random number list on the graphing calculator, use the following keys: ENTER MATH RandInt Create a random number generator for the integers 1 to 10 Input: (1, 10)

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