Probability: Compound Events
Objectives
SWBAT:
• Explore and determine the probabilities of compound events: independent and dependent/conditional events
Feb 26­10:30 PM
Compound Events: Independent events
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Feb 20­2:25 PM
Feb 26­6:23 PM
Compound Events: a combination of 2 or more events
ex: toss a coin and roll a die
spin a color spinner and a number spinner
1
2
4
3
pick a name from a hat and then pick another name
Feb 26­10:30 PM
Compound Events (Independent)
Independent events: outcome of one event does not affect the outcome of the other event Example 1: toss a coin and roll a die
P (Heads) and P (2) =
1/2 x 1/6 = 1/12 Example 2: bag contains 10 marbles: 3 red, 5 blue, 2 green
Pick a marble from the bag, replace the marble, and pick again P (red) and P (green) = P (red and green)
3/10 x 2/10 = 6/100 or 6 %
P (A and B) = P(A) x P (B)
Feb 26­10:30 PM
"Color ­ Number Spins"
Feb 26­10:49 PM
Compound events (Dependent or Conditional)
Dependent or Conditional events: the outcome of the 2nd event depends on the outcome of the 1st event
Ex: bag contains 10 marbles: 3 red, 5 blue, 2 green
Pick a marble from the bag, do NOT replace the marble, then pick again P (red, then green) = P(red) x P(green after red) = 3/10 x 2/9
= 6/90 = 1/15
P (A, then B) = P(A) x P(B after A)
Feb 26­10:30 PM
Mike has a bag with 16 marbles: 8 black, 5 red, and 3 multi­color
Find the probability of Mike picking:
a marble that is not black
a black marble, not replacing it, then picking a multi­color one
a red marble, replacing it, then picking another red
a multi­color, then a red, then a black (without replacing after each pick)
Feb 26­10:30 PM
Forrest has a box of 20 chocolates which all look alike. 12 have cherry cream filling, 5 have vanilla cream filling, and 3 have orange cream filling.
Find the probability of Forrest choosing and eating:
an orange cream
an orange cream, then a vanilla cream
2 cherry creams in a row
What would the probability be if Forrest
chose a cherry cream, put it back in the box, then chose a vanilla cream?
Feb 26­10:30 PM
Mar 1­1:05 PM