Independent and Dependent Events: Probability
1 Hook and Introduction
As soon as students are in class, have all students stand up and give each a coin. Tell them, "You're going to play 'Tails never Fails.' In this game, if a student tosses and gets 'tails'; he/she stays in the game. Keep track of how many times you have tossed the coin before you have a winner.
In this coin-toss game, students begin to understand a compound event and the probability of getting n tosses in a row. They really get excited by the possiblity of someone getting tails more than a few times in a row.
For support, watch the video:https://www.teachingchannel.org/videos/teaching-probability-odds
To follow up the game, indicate that now we're going to play "3."
Using a bag of popsicle sticks ( or bag with slips of paper, or a random number generator) with each students name on a stick, choose who gets to throw a die to try and get the number "3" (or pick your favorite number between 1-6). Don't replace the stick, and have the next student chosen try. Each time you choose a name, ask what the liklihood or probability of a the next student to be chosen, and follow up with why? Once several students have been chosen, ask how this is different than the coin toss game, or throwing the die.
- Everyone stand at your desk
- Take a coin
- "Tails never Fails." - Flip the coin and if you get tails you stay standing.
2 Formative Assessment: Independent vs. Dependent
Use socrative to ask the difference between a set of independent vs. dependent events (T/F)
3 Mini-Lesson (Direct Instruction)
Review the game and have students determine that in a compound, independent event, the probability is P(A) * P(B) occuring. for example, with the coin toss it is 1/2 * 1/2 for P(Heads) each toss.
Determine how a compound, dependent event differs.
P(A)* P(B after A)
4 Guided Cooperative Practice
Students practice determining whether an event is independent or dependent, and apply the correct algorithm. This is done in dyads or small groups.
Watch the Brain-Pop video on Independent and Dependent Events and take the quiz using Socrative or Formative to record results. If you want to use a more robust option. You can create an exit slip to determine exactly how much a student understands about using the algorithms of P(A)*P(B) vs. P(A )* P(B after A)
Key Standards Supported
Statistics And Probability
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?