Quiz Tomorrow! Warm-Up… Quickwrite… If your eyesight became severely bad, would you get stronger glasses/contact lenses or LASIK surgery? Why? Ex: “If my eyesight became severely worse, I would choose _________ because ________________________________________________.”

Compare and Explain… your Warm-Up starting with Student #1 (1 min) 0.639 Not really.

Round Robin… starting with the student who sits closest to the board at your table (1 min) If your eyesight became severely bad, would you get stronger glasses/contact lenses or LASIK surgery? Why? Ex: “If my eyesight became severely worse, I would choose _________ because ________________________________________________.”

Homework Answers 11. a) 0.082 b) 0.918 12. a) 0.028 b) 0.972 13. b) Yes!

Probabilities for a binomial experiment

Probability of a Range of Successes In such cases, we need to use the addition rule for mutually exclusive events Ex: For n = 6 and p = 0.50, P(4 or fewer successes) = P (r  4) = P (r = 4 or 3 or 2 or 1 or 0) = P(4) + P(3) + P(2) + P(1) + P(0)

Is there another way? Notice that P(4) = 0.234 Excerpt from Table 3 of Appendix II for n = 6

For n = 6 and p = 0.50, P (r  4) = P(4) + P(3) + P(2) + P(1) + P(0) = 0.234 + 0.312 + 0.234 + 0.094 + 0.016 = 0.890 We can also use the fact that the total of all P (r) values for r between 0 and 6 is 1 and the complement rule Since the complement of the event r  4 is the event r  5, P (r  4) = 1 – P(5) – P(6) = 1 – 0.094 – 0.016 = 0.890

Example: Hybrid Tomato It is known that the seeds of a hybrid tomato have probability 0.70 of germinating, and a biologist plants six seeds What is the probability that exactly four seeds will germinate? This is a binomial experiment with n = 6 trials: each seed planted represents an independent trial We’ll say germination is success, so the probability for success on each trial is 0.70

n = 6 p = 0.70 q = 0.30 r = 4 P(4) = 0.324 Excerpt from Table 3 of Appendix II for n = 6

Example What is the probability that at least four seeds will germinate? In this case, we are interested in the probability of four or more seeds germinating This means we are to compute P (r  4) The events are mutually exclusive, so we can use the addition rule P (r  4) = P (r = 4 or r = 5 or r = 6) = P(4) + P(5) + P(6) We already know the value of P(4), so we find P(5) and P(6)

Example P(5) = 0.303 and P(6) = 0.118 Now we have all the parts necessary to compute P (r  4). P (r  4) = P(4) + P(5) + P(6) = 0.324 + 0.303 + 0.118 = 0.745

Homework