Math 7 Domain: Statistics and Probability
Day 4A
Learning Outcome – Students will be able to find compound probabilities by multiplying together the simple probability for each event.
Clusters/Standards
7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
7.SP.8.a 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.
7.SP.8b 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.
7.SP.8.c 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?
Activities
This is already in your note packet:
Dependent Events are two events in which the outcome of the first affects the outcome of the second.
Independent Events are two events in which the outcome of the first has no effect on the outcome of the other event.
Think Now:
Label each pair of events as Dependent or Independent.
a)Getting a heads on a coin and rolling a 5 on a die. Independent
b)Drawing a 4 from a deck of cards, then drawing another 4 without replacing the first. Dependent
c)Drawing a queen, replacing it and drawing another queen. Independent
Discuss “dependent and independent” as it applies to the students’ lives.
Go over Do now
Project Preptask answers and take questions.
Today we will be discussing Probability of Compound Events
WATCH) Draw a tree diagram to show the total number of outcomes: I have 2 Black marbles and 1 White. How many ways can I pick 2 marbles if I put the first one back before I pick the next (with replacement).
BB B 9 possible outcomes
BBB B
WB WP(B,B)? 4/9
BB BWhat is the P(B) for Pick #1? 2/3
BBB BWhat is the P(B) for Pick #2? 2/3
WB WAre these events Independent or Dependent?
BW B Independent: 2/3*2/3=4/9
WBW B
WW W
(without replacement)
BB B 6 possible outcomes
B
WB WP(B,B)? 2/6=1/3
BB BWhat is the P(B) for Pick #1? 2/3
BWhat is the P(B) for Pick #2? 1/2
WB WAre these events Independent or Dependent?
BW B dependent: 2/3*1/2=2/6
WBW B
Tree diagrams are not needed.
NOTES
Formula to find the probability of compound events :
P (A and B)=P(A) x P(B)
Ex1) a bag has 4 choc chip cookies, 5 oatmeal and 1 peanut putter
Find the probability that Julia picks an oatmeal cookie, eats it, and then Joanne picks an oatmeal cookie if they pick without looking.
First Pick: P(oatmeal)=5/10=1/2
Second Pick: P(oatmeal) =4/9 Dependent Events!
P(2 oatmeal cookies)=1/2 * 4/9=4/18 = 2/9
Ex2) 2 dice are rolled. Find:
P(odd#, 4) ask if these are independent or dependent events
P(odd)=1/2
P(4)=1/6
P(odd,4)=1/2*1/6=1/12
Ex3) 2 cards are drawn from 9 cards numbered 2-10. Once a card is selected it is not replaced. (dependent)
P(10,2)=1/9 * 1/8 = 1/72
P(2 #s >7)=3/9 * 2/8 = 6/72 = 1/12
Pass out preptask and let students start in class. Monitor.
Closure: How can you find the probability of more than 1 thing happening? What if they are dependent?
PrepTask: Worksheet 13-6 “Probability of Two Events”
Evaluation: PrepTasks, Class Participation, Quiz