Transcript Number of Possible Outcomes

NUMBER OF POSSIBLE
OUTCOMES
• Probability and Statistics 3.1* Represent all possible
outcomes for compound events in an organized way (e.g.,
tables, grids, tree diagrams) and express the theoretical
probability of each outcome.
• Objective: Understand and be able to apply the formula
for calculating the number of possible outcomes
• Learning target: Answer at least 3 of the 4 probability
questions correctly on the exit ticket.
• What is a tree
diagram?
• A way to list all the possible
outcomes of MULTIPLE events.
• Start with a dot, then draw one
branch for every outcome of the
first event.
• From each of those branches, draw
a branch for every outcome of the
second event, and so on.
• I roll a die, then flip
a coin. Draw a
tree diagram.
• Event 1 (rolling a die) has 6
outcomes, so draw 6 branches.
• Event 2 (flipping a coin) can be heads
or tails. From each of the previous
branches, create a heads and a tails
branch. This means you will
repeat the
outcomes
multiple
times.
• I flip a coin, then
choose either rock,
paper, or scissors.
Draw a tree
diagram to find the
number of
possibilities.
• Tree diagrams are great for small numbers, but can you
imagine the tree diagram for events with 10+ outcomes
each?
• It would waste a lot of time and writing and it would get too
crowded to be able to read
• We need to figure out a shortcut for calculating the number
of possible outcomes
• Notice that the group of 3 appears 2 times?
• How many times did the group of 2 appear?
• Why did the group appear that many times?
• Does it still work if there’s more than 2 events?
• Does it still work if there’s more than 2 events?
• There are three choices of pants
• Mathematical calculation: 3
• Does it still work if there’s more than 2 events?
• No matter which pants you chose, you can choose any of
the 4 shirts
• Mathematical calculation: 3 × 4
• Does it still work if there’s more than 2 events? Yes!
• No matter which pants and shirt you chose, you choose
either of the 2 shoes
• Mathematical calculation: 3 × 4 × 2 = 24 possible outcomes
• How do we find the
total number of
outcomes for
multiple events?
• I have 8 shirts and
9 ties. I pick one
of each. How
many possible
outcomes?
• Multiply together the number of
outcomes for each event.
• 8×9 = 72
• I pick one of my 5
hats, one of my 3
scarves, and one
of my 2 shoes.
How many
different outfits are
possible?
• 5×3×2 = 30
Collaborative Station
• You must calculate the number of possibilities for each
problem.
• 1) I have ___ shirts and ___ pants. If I pick one of each,
the number of different outfits is ____.
• Fill in the first blanks with your own numbers. Then
calculate the number that goes in the last blank using our
shortcut.
• If any of your numbers are 0, use 1 instead.
Independent Station
• You will continue ST Math’s unit on probability.