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Intro to Probability

Intro to Probability. Notes 15. Probability. Probability – a number from 0 – 1 that represents the likelihood an event will happen. Can also be written as a percent. Helps us to make inferences and predict the outcome of an event in order to make informed decisions. Probability Outcomes. ½.

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Intro to Probability

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  1. Intro to Probability Notes 15

  2. Probability • Probability – a number from 0 – 1 that represents the likelihood an event will happen. Can also be written as a percent. • Helps us to make inferences and predict the outcome of an event in order to make informed decisions.

  3. Probability Outcomes ½ 0 1 Equally likely to occur Impossible to occur Certain to occur 50 % 0% 100%

  4. Theoretical vs. Experimental • Theoretical probability – each outcome has an equally likely chance of happening. It is what should occur. • Experimental probability – probability calculated using data collected in an experiment. It is what actually occurs when an experiment is repeated many times.

  5. Finding Probability • The formula for probability is: • “Or” → add each probability together • “And” → multiply each probability together

  6. Example 1 Calculate each probability using the spinner. P(red) P(green or blue)

  7. Example 1 cont. Calculate each probability using the spinner. P(black and then green) P(blue and then green or red)

  8. Counting How many possible outcomes are there? Tossing 4 coins? Rolling 3 dice?

  9. Example 2 Three coins are tossed. How many possible outcomes? Find P(HTH) Find P(all same side)

  10. Example 3 Kate has 3 jeans (light, medium, dark), 4 shirts (pink, blue, purple, white) and 2 pairs of shoes (converse and boots). How many outfits are possible? Find P(light or dark, white or pink, converse)

  11. Example 4 A deli has 4 kinds of bread, 5 kinds of meat, and 3 kinds of cheese. How many different sandwiches are possible with one bread, meat, and cheese?

  12. Independent vs. Dependent • Independent events: the occurrence of one event has no effect on the occurrence of the other event. • Dependent events: the occurrence of one event affects the occurrence of the other event.

  13. Independent vs. Dependent • Consider choosing objects from a group of objects. If you replace the object each time, choosing additional objects are independent events. • If you do not replace the object each time, choosing additional objects are dependent events.

  14. Independent vs. Dependent • Determine whether the events are independent or dependent: • One coin is tossed, and then a second coin is tossed. • Wednesday’s lottery numbers and Saturday’s lottery numbers. • Andrea selects a shirt from her closet to wear on Monday and then a different shirt to wear on Tuesday.

  15. Probability of 2 Independent Events • If two events A and B are independent, then P(A and B) = P(A) * P(B)

  16. Example 5 • A coin is tossed and a die is rolled. What is the probability that the coin lands heads up and the number rolled is a 6?

  17. Example 6 • Suppose you toss a coin four times. What is the probability of getting four tails?

  18. Probability of 2 Dependent Events • If two events A and B are dependent, then P(A and B) = P(A) * P(B|A) P(B|A): probability that event B occurs given A has already occurred

  19. Example 7 • In a bag is 3 green and 4 blue marbles, a blue marble is drawn and not replaced. Then a second blue marble is drawn. Find the probability of this outcome:

  20. Assignment Counting – Probability WS Missed the Test? See Mrs. James today! Math’s Mate 3-2

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