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Basic Statistics & Probability

Basic Statistics & Probability

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Introduction to :

Complementary events are two outcomes of an event that are the only two possible outcomes.

  • This is like flipping a coin and getting heads or tails. Of course, there are no other options, so these events are complementary.
  • Rolling a die and getting a 1 or 2 are not complementary, since there are other outcomes that may happen (3, 4, 5, or 6).
  •  However, rolling a die and getting a 1 or not-a-1 are complementary (you have to roll either a 1 or not-a-1).

Mutually exclusive events are two or more outcomes of an event that cannot occur at the same time.

  • Picking one card from a standard deck and choosing an ace or a king are mutually exclusive events (since you can't do both at the same time).
  • However, choosing a red card or a king are not mutually exclusive (you could choose a red king).

All complementary events are mutually exclusive, but all mutually exclusive events are not necessarily complementary.

Instructions

Let's note each Example as complementary, mutually exclusive, both, or neither.

piggy bank

Note: the piggy bank contains a Quarter (25 cents), Dime (10 cents), Nickel (5 cents), and Penny (1 cent)


Example 1

Picking one coin from the piggy bank and getting a dime or a nickel.

Mutually exclusive? Yes. You can't pick a dime and a nickel at the same time

Complementary? No. There are other options, like a penny or quarter


Example 2

Picking a coin from the piggy bank and getting a quarter or a coin divisible by 5.

Mutually exclusive? No

Complementary? No

Quarters are also divisible by 5 (as well as dimes and nickels), so these are not mutually exclusive nor are they complementary.


Example 3

Choosing one marble from the bag and getting a blue or a green one.

Mutually exclusive? Yes. You can't choose a marble that is both blue and green at the same time.

Complementary? No. There are other options (like an orange one).


Classify each event as complementary, mutually exclusive, both, or neither:

dice

Exercise 1

Rolling a die and getting an odd number or a 4.

Exercise 2

Rolling a die and getting an even number or a four.

Exercise 3

Rolling a die and getting an odd number or an even number.

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