- The Counting Principle states that if two experiments are performed, where the first experiment can have m outcomes and the second experiment can have n outcomes, then there are a total of m×n outcomes.
- We have already discussed this with tossing two dice.
The first die can have 6 different outcomes
The second die can have 6 different outcomes
There are a total of 36 different outcomes.
- If I have two different pants (jeans-j and dockers-d) , and 3 different shirts (dress-d, polo-p, t shirt-t, how many different outfits can I wear?
number of pants = 2
number of shirts = 3
Total combinations = 2*3 = 6
- We can draw a diagram to help us find all different possibilities.
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- When conducting an experiment where something is selected, then something else is selected, we use the term replacement
- If after you select something, you put it back this is called with replacement
- If after you select something, you don't put it back, it is called without replacement
- The replacement policy changes the probability
- If I have a bag with three red balls and two blue balls, what is the probability of selecting two red balls without replacement.
There are 5*4 or 20 possibilities
Of these 2 are blue followed by blue, or 2/20 or 1/10 or 10%.
- Same problem but with replacement
There are now 5 * 5 or 25 possibilities.
Of these, 4 are blue blue, or 4/25 or 16%.
- A coin is tossed, if it is heads, a 6 sided dice is tossed, if it is tails, a 4 sided dice is tossed. What is the probability of
Tossing a 1
Draw the tree diagram.
Note there are 10 possibilities
There are two ways to get a 1 H-1, T-1
P(1) = 2/10 or 1/5 or 20%
Tossing a 6
There is one way to get a 6 H-6
P(6) = 1/10 or 10%