Independent and Dependent Events Slide 1

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 (eg.: 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 2

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 3

Dependent Event What happens the 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 4

Dependent Event Example: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first, what is the probability that you will get 2 black pens? P(black first) = P(black second) = (There are 13 pens left and 5 are black) THEREFORE……………………………………………… P(black, black) = Slide 5

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. 2. You have a bag of marbles: 3 blue, 5 white, and 12 red. You choose one marble out of the bag, look at it then put it back. Then you choose another marble. 3. You have a basket of socks. You need to find the probability of pulling out a black sock and its matching black sock without putting the first sock back. 4. 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 tile. Slide 6

Independent Events Find the probability 1 5 5 8 P(jack, factor of 12) 40 x = 1 8 Slide 7

Independent Events Find the probability 5 5 1 36 6 6 P(6, not 5) x = Slide 8

Dependent Events Find the probability 1 26 25 650 P(Q, Q) All the letters of the alphabet are in the bag 1 time Do not replace the letter 1 26 25 650 x = Slide 9