Independent and Dependent Events Compound Events Lessons 11-7 & 11-9

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 two events are unrelated Independent Events #1 The two events are unrelated P(choosing a jack, rolling a 2) P (spinning a 3, pulling an ace) P (rolling a 6, spinning a red)

Independent Events #2 You repeat an event with an item whose numbers will not change (e.g.: spinners, dice, flipping a coin, etc.)

Independent Events #3 You repeat the same activity by pulling something out, but you REPLACE the item that was removed.

Dependent Event 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.

Dependent Event Look for the following 2 clues to determine if an event is dependent You repeat the same event You remove something after the first event and DO NOT REPLACE it. You ask yourself the question, “What happens second?” and your answer is “It depends...”

Representing and Solving for a Compound Event Two events are listed and there is a comma in between them. P(yellow, yellow) P(heads, tails) P(6, even number) P(not 6, not 5) Events must occur in the order listed. Figure out the probability of the first event and multiply it by the probability of the second event. Remember that the probability of a second event changes in dependent events. It does not change with an independent event.

Solving Independent Events When you have two independent events: Find the probability of the first event Find the probability of the second event Multiply the probabilities together Reduce your answer Remember that the two events have nothing to do with one another because they involve 2 separate items OR one item, but things are replaced after the first draw.

An Independent Event 3 10 2 10 1 5 3 50 P(yellow, red) Yellow: There are 10 socks in a basket: 5 blue, 3 yellow and 2 red. What is the probability of choosing a yellow sock and a red sock if the sock is replaced after the first event? is replaced P(yellow, red) Yellow: Replace the yellow sock. Red: 3 10 x 2 10 1 5 3 50 =

Solving Dependent Events When you have two dependent events: Find the probability of the first event Figure out what has changed Numerator and/or denominator Figure out the probability of the second event Multiply the 2 probabilities together Reduce your answer Remember that the two events are interconnected. Items are NOT replaced after being pulled out.

Notice that the denominator changed A Dependent Event There are 10 socks in a basket: 5 blue, 3 yellow and 2 red. What is the probability of choosing a yellow sock and a red sock if the sock is NOT replaced after the first event? is NOT replaced P(yellow, red) Yellow: DO NOT replace the yellow sock. Red: 3 10 Notice that the denominator changed x 2 9 6 90 1 15 =

Are these dependent or independent events? TEST YOURSELF Are these dependent or independent events?

Are these dependent or independent events? Tossing two dice and getting a 6 on both of them. Independent Event

Are these dependent or independent events? 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. Dependent Event

Are these dependent or independent events? 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. Independent Event

Are these dependent or independent events? You pick the letter W from a bag containing all the letters of the alphabet. You put the W back in the bag and pick a second time. Independent Event

Are these dependent or independent events? 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. Dependent Event

Find the probability 1 5 2 8 2 40 x = P(jack, green) 1 20

Find the probability 1 6 5 6 5 36 x = P(6, not 5)

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

Find the probability P(striped, striped) The num. changed to a 4 because you pulled out a striped marble. Now the bag is missing one. P(striped, striped) There are 10 marbles in the bag: 5 striped 5 solid Do not put the first marble back. 5 10 4 9 20 90 x = The denominator changed to a 9 because we have one less marble in the bag since we did not put it back! 2 9