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Probability of Independent Events

Probability of Independent Events. Coach book pgs. 238 – 243 Math book pgs.634 – 639 GALT pgs. 253 – 257. Vocabulary. Probability - a way to measure the chance that an event will occur P = the number of favorable outcomes the number of possible outcomes

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Probability of Independent Events

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  1. Probability of Independent Events Coach book pgs. 238 – 243 Math book pgs.634 – 639 GALT pgs. 253 – 257

  2. Vocabulary • Probability - a way to measure the chance that an event will occur P = the number of favorable outcomes the number of possible outcomes • Independent Event – 2 or more events that do not have an effect on the outcomes of each event (Example: rolling a die and flipping a coin)

  3. How to write probability P = the number of favorable outcomes the number of possible outcomes In this form, probability is written as a fraction. Remember to always write fractions in their simplest form. Probability can also be written as a decimal or percent.

  4. How to write probability (continued) … Write the following probability as a fraction in simplest form, a decimal, and a percent. What is the probability of rolling an even number on a die? Number of even numbers on a die = Total numbers on a die = Probability (even number) =

  5. You toss a coin and roll a number cube. What is the probability that you flip heads and roll an odd number? Ask yourself: What are the different outcomes that I could have by tossing a coin and rolling a number cube? You can make a tree diagram to see this… First event Second Event All possible Outcomes H1, H2, H3, H4, H5, H6 Heads Roll 1,2,3,4,5, or 6 Tails Roll 1,2,3,4,5, or 6 T1, T2, T3, T4, T5, T6

  6. Out of all of the possible outcomes, how many match the given situation? How many outcomes are possible? How many of these match our two criteria (heads and odd)? What is the probability of flipping a heads and rolling an odd number? P = number of favorable outcomes number of possible outcomes

  7. There is a shortcut…  For independent events, the probability that both events occur is the product of the probabilities of the events. If you want to flip heads and roll an odd number, you figure the probabilities of each event and multiply them. P (flipping heads) • P (rolling an odd number) = P (heads and odd number) 1•3 = 3 = 1 2 6 12 4

  8. A computer randomly generates 4-digit passwords. Each digit can be used more than once. What is the probability that the first and second digits are both 1? Probability of the first digit being 1 Probability of the second digit being 1 Probability of the both digits being 1 • = 1 10 1 10 1 100 • =

  9. Try it on your own … The weather report stated that the chance of rain today is 50% and the chance of rain tomorrow is 30%. What is the probability that it will rain both days?

  10. What is the probability of flipping a nickel, dime, and quarter and having them all land heads up?

  11. Caitlyn has 25 red ribbons, 10 black ribbons, and 15 pink ribbons in a paper bag. She draws a ribbon at random from the bag, returns it to the bag, and then draws a second ribbon. What is the probability that the first ribbon is red and the second ribbon is black?

  12. Practice Assignment GALT pgs. 256 – 257 (1, 3, 4, 8, 9) Graded Assignment Coach pgs. 242 – 243 (1 – 8)

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