Review: Equally Likely Outcomes Mini-Quiz What is the likelihood of spinning a 2? a. as a ratio b. as a fraction c. as a decimal d. as a percent 2. Are 1, 2, 3, 4, 5, 6, 7, 8 Equally Likely Outcomes?

Objective: The student will be able to calculate the Probability of an event; identify the difference between Independent versus Dependent Events; Calculate the Probability of two Independent Events; and Calculate the Probability of two Dependent Events.

Independent versus Dependent Events Slide 3

What is the Probability of spinning a 2?   What is the Probability of spinning a 2?

Independent Events Whatever happens in one event has absolutely nothing to do with what will happen next because: The two events are unrelated OR You repeat an event with an item whose numbers will not change (i.e. spinners or dice) You repeat the same activity, but you REPLACE the item that was removed. The probability of two independent events, A and B, is equal to the probability of event A times the probability of event B. Slide 5

Independent Events Example: Suppose you spin each of these two spinners. What is the probability of spinning an even number and a vowel? P(even) = (3 evens out of 6 outcomes) P(vowel) = (1 vowel out of 5 outcomes) P(even, vowel) = S T R O P 1 2 3 6 5 4 Slide 6

Dependent Events What happens during the second event depends upon what happened before. In other words, the result of the second event will change because of what happened first. The probability of two dependent events, A and B, is equal to the probability of event A times the probability of event B. However, the probability of event B now depends on event A. Slide 7

Dependent Events Example: There are 6 black pens and 8 blue pens in a jar. If your friend mixes up the pens in the jar and you close your eyes and take a pen out of the jar and put it on a table and then take another pen out of the jar, what is the probability that you will get 2 black pens? (The pens are all the same basic style.) P(black first) = P(black second) = (There are 13 pens left and 5 are black) THEREFORE……………………………………………… P(black, black) = = Slide 8

Are these dependent or independent events? TEST YOURSELF Are these dependent or independent events? Tossing two dice and getting a 6 on both of them. You have a bag of marbles: 3 blue, 5 green, and 12 red. Find the probability of choosing a red marble and then a green marble. Choose one marble out of the bag, look at it, then put it back. Then you choose another marble. You have a basket of socks. You need to find the probability of pulling out a blue sock and its matching blue sock without putting the first sock back. You pick the letter Q from a bag containing all the letters of the alphabet. You do not put the Q back in the bag before you pick another letter. Slide 9

Independent Events Answer: Find the probability 1 5 5 8 5 40 P(jack, factor of 12) x = 1 8 Answer: Slide 10

Independent Events Find the probability 5 5 1 36 6 6 P(6, not 5) x = Slide 11

Dependent Events Find the probability P(Q, Q) All the letters of the alphabet are in the bag Do not replace the letter 1 26 25 650 x = Slide 12

Lesson Summary: Objective: The student will be able to calculate the Probability of an event; identify the difference between Independent versus Dependent Events; Calculate the Probability of two Independent Events; and Calculate the Probability of two Dependent Events.

Objective: The student will be able to identify Combined Events. Preview of the Next Lesson: Objective: The student will be able to identify Combined Events.

Homework Statistics HW 9 and HW 7