Dependent and Independent Events Section 4.2

Objectives Understand the difference between dependent and independent events. Explain why a scenario is dependent or independent.

Independent and Dependent Events Two events are independent if the occurrence or nonoccurrence of one event does not change the probability that the other will occur. If the events are dependent, then we must take into account the changes in the probability of one event caused by the occurrence of the other event.

Example – Dependent or Independent Events Claire bought two coffees from Starbucks and a pair of shoes from Famous Footware. Are the events dependent or independent? Explain. Solution: Independent Buying coffee has no bearing on what kind of shoes she buys. Because the one event does not change the other event they are independent.

Example – Dependent or Independent Events You roll a standard die twice. What is the probability of getting an even number and then a five. Are the events dependent or independent? Explain. Solution: Independent Rolling a standard die one time will not take out any possibilities on the second roll. Because the one event does not change the probability of the other event they are independent.

Example – Dependent or Independent Events Ben has $200. He bought a microwave worth $120. He wanted to buy a iphone, but didn’t have enough money, so he bought an ipod instead for $75. Are the events dependent or independent? Explain. Solution: Dependent After buying a microwave, Ben has limited options of what else he could purchase. Because one event happened he could not purchase an iphone, so the events are dependent.

Example – Dependent or Independent Events Robin has some balls in a bag. She picks a ball at random. Without putting the first ball back, she picks the second ball at random. Are the events dependent or independent? Explain. Solution: Dependent After picking one ball out, Robin can no longer pick that particular ball out again, so she has limited options of what she can pick next. Because one event happened and the next event is now limited, so the events are dependent.

Example – Dependent or Independent Events You have a jar with 24 pieces of chocolate candy and 14 pieces of orange candy. I take one piece out and eat it. Then you take a piece and eat it. Are the two events dependent or independent? Explain. Solution: Dependent After picking out a piece of candy, I ate it. That means that you cannot pick that piece of candy, so you are limited to what you can pick. Because one event happened and the next event is now limited, the events are dependent.

Example – Dependent or Independent Events Denny has a blue tie, a red tie, and a green tie. He also has a blue shirt and a green shirt. Denny chooses a random tie and a random shirt for work today. Are the events dependent or independent? Explain. Solution: Independent After randomly picking a tie, Denny then randomly picks a shirt. Because picking a tie has no impact on what shirt he pick, the events are thus independent.

Example – Dependent or Independent Events Amy plays card games and is quite accomplished at most of them. She picks a card at random. Then without putting the first card back she picks a second card. Are the events dependent or independent? Explain. Solution: Dependent After picking a card, Amy didn’t put the card back so she cannot pick that card again. Because picking the first card changes what she can pick for the second card, thus the events are dependent.

Example – Dependent or Independent Events Joe has 14 football cards. He takes three of them at random, then he picks two more and gives them to his little sister. Are the events dependent or independent? Explain. Solution: Dependent Since Joe picked his three cards first, and didn’t give his sister the option to pick those cards, the events are dependent.

Example – Dependent or Independent Events Jeff has three children. His first two children are boys, and his last child is a girl. Are the events dependent or independent? Explain. Solution: Independent Each child has an equal chance of being a boy or a girl. Therefore, because having a boy first and second has no impact on the gender of the third child, the events are independent.

4.2 Dependent and Independent Events Summarize Notes Read section 4.2 Homework Worksheet