1. First lecture
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Faten alamri

2. Old saying
“probability is the most important concept in modern science especially as nobody has slightest notation what it means”
Counting techniques
1) multiplication rule 2) computation )permutation
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3. P(A) = N(A)\N(S)
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Note: these are called “counting methods” because we have to count the number of ways A can occur and the number of total possible outcomes.

4. Example 1: You draw one card from a deck of cards
Example 1: You draw one card from a deck of cards. What’s the probability that you draw an ace?
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5. What's the probability of 2 heads when tossing a coin?
Example
What's the probability of 2 heads when tossing a coin? H T
Toss 1:
2 outcomes
Toss 2:
22 total possible outcomes: {HH, HT, TH, TT}
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6. What’s the probability of rolling a die then tossing a coin?
Example
What’s the probability of rolling a die then tossing a coin?
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7. Permutations—order matters!
Counting methods for computing probabilities
Permutations—order matters!
Combinations—
Order doesn’t matter
With replacement
Without replacement
Without replacement
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8. Formally, “order matters” and “with replacement” use powers
Example
How many license plates can we have using three letters followed by three digits ?
Alphabet 26 digit # 10 =
=(17576)(1000)
=17,576,000
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9. Permutation: The number of ways in which a subset of objects can be selected from a given set of objects, where order is important
Example 1.6 pg5
Example
From a club of 24 members, a President, Vice President, Secretary, Treasurer and Historian are to be elected. In how many ways can the offices be filled?
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10. Answer
Example 1.4. How many permutations are there of all three of letters a, b,
and c?
Answer:
= n!\(n − r)!
=3!\0!
= 6
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11. Combinitions
Combination: The number of ways in which a subset of objects can be selected from a given set of objects, where order is not important.
A Combination is an arrangement of items in which order does not matter.
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Since the order does not matter in combinations, there are fewer combinations than permutations.  The combinations are a "subset" of the permutations.

12. To find the number of Combinations of n items chosen r at a time, you can use the formula
c is denoted by
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13. Example 1.7 pg 5
Example
To play a particular card game, each player is dealt five cards from a standard deck of 52 cards. How many different hands are possible?
Answer
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14. Guidelines on Which Method to Use
2/22/2019
Guidelines on Which Method to Use
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