Review: Mini-Quiz Combined Events Question: A box contains three cards numbered 1, 3, 5. A second box contains four cards numbered 2, 3, 4, 5. A card is chosen at random from each box. (a) Show all the possible outcomes of the experiment using a possibility diagram or a tree diagram. (b) Calculate the probability that (i) the numbers on the cards are the same, (ii) the numbers on the cards are odd, (iii) the sum of the two numbers on the cards is more than 7. Slide 1

Class Greeting

Objective: The student will be able to calculate the Probability of A and B and the Probability of A or B.

Probability of A and B P(AB) and Probability of A or B P(A or B)

(3 evens out of 6 outcomes) The probability of two independent events, A and B, is equal to the probability of event A times the probability of event B. Example: Suppose you spin each of these two spinners. What is the probability of spinning an even number and a vowel? S T R O P 1 2 3 6 5 4 P(even) = (3 evens out of 6 outcomes) P(vowel) = (1 vowel out of 5 outcomes) P(even, vowel) = Slide 5

P(A OR B) = P(A U B) = P(A) + P(B) Addition Rule A and B are mutually exclusive The occurrence of one event precludes the occurrence of the other Addition Rule P(A) P(B) P(A OR B) = P(A U B) = P(A) + P(B)

The probability of being either blood type O or blood type A Example Blood Group Males Females Total O A B AB 20 17 8 5 18 7 40 35 15 10 50 100 The probability of being either blood type O or blood type A P(OUA) = P(O) + P(A) = (40/100)+(35/100) = 0.75

P(A OR B) = P(A U B) = P(A) + P(B) - P(A ∩ B) A and B are not mutually exclusive (Can occur together) Example: Male or Blood Type O Modified Addition Rule P(A) P(B) P(A ∩ B) P(A OR B) = P(A U B) = P(A) + P(B) - P(A ∩ B)

Example: Two events are not mutually exclusive (male gender and blood type O). P(M OR O) = P(M)+P(O) – P(M∩O) = 0.50 + 0.40 – 0.20 = 0.70

If “Noodles” are served 20% of the time for teachers lunch, (a) Find the probability that “Noodles” would be served on two randomly selected days (the two events are independent)   (b) If two days are selected randomly what is the probability that at least one of those days will be a Noodle Day?   (c) If two days are selected randomly what is the probability that only one of those days will be a Noodle Day?  

Lesson Summary: Objective: The student will be able to calculate the Probability of A and B and the Probability of A or B.

Preview of the Next Lesson: Objective: The student will be able to identify the Complement of an event and calculate the probability of the Complement of an event.

Statistics HW 11 and HW12 and HW 7 Homework Statistics HW 11 and HW12 and HW 7