Chapter 10 Probabilities

Question 1

Ch 10-1

Define the Fundamental Counting Principle

Answer 1

The Fundamental Counting Principle is used to see how likely a possible outcome will happen. Multiply all the possible outcomes together. (Watch for the word “and” in the description.) Exception: Mutually exclusive situations.

Question 2

Ch 10-1

Define Mutually Exclusive

Answer 2

If possibilities cannot be done at the same time, they are mutually exclusive. To calculate probabilities add them together.

Question 3

Ch 10-1

Compare the probability issues Repetition and Non-Repetition

Answer 3

Repetitions means the same possibilites happen everytime you do it.
Non-repetitions mean that each time you do it, you reduce the chance by a certain amount.

Example of non-repetition: Throw away 1 card each time you pick a card.

Question 4

Ch 10-2

Define permutations when repetition is ok. Write the formula.

Answer 4

All permutation formulas mean that order matters. There are two kinds: repetition is allowed; repetition is not allowed. Permutation formula for allowed repetition is n^r. N is the number of objects raised to the power of r the number of choices.

Question 5

Ch 10-2

Define permutations when repetition is NOT ok. Write the formula.

Answer 5

All permutation formulas mean that order matters. When repetition is not allowed use this formula _nP_r = n!/n-r!

Question 6

Ch 10-2

Define combinations when repetition is ok. Write the formula.

Answer 6

In combinations order does not matter. When repetition is allowed use the formula (n + r-1)!÷r!(n-1)! n is the number of objects and r is the number of choices.

Question 7

Ch 10-2

Define combinations when repetition is NOT ok. Write the formula.

Answer 7

In combinations order does not matter. When repetition is not allowed use the formula _nC_r which is n!÷r!(n-r)! n is the number of objects and r is the number of choices.

Question 8

Ch 10-3

Explain four terms used in Probability math

Answer 8

• Probability–how likely it is that something will happen
• Trial–a single repeatable experiment where the same thing is done over and over
• Outcome–the result of a trial
• Event–the outcome of one or more trials.

Question 9

Ch 10-3

Find probability

Answer 9

The number of favorable outcomes divided by the number of possible outcomes.

Question 10

Ch 10-3

Determine a simple event

Answer 10

Only one outcome at a time is possible, though they might be different each time.

Question 11

Ch 10-3

Determine the probability of a compound event, meaning more than one outcome is possible.

Answer 11

• Determine the probability of each outcome
• Multiply all the probabilities together.

Question 12

Ch 10-3

Explain complementary events and write the formula

Answer 12

In complementary events only one outcome can and must occur and the other outcome cannot occur. If you take the outcome you will get plus the outcome you will not get, that’s the whole possibility. If you account for 1/1 or 2/2 or 3/3, etc, they always equal 1. The formula is the possibility of the first one + the possibility of the second one = 1. P(a) + P(b) = 1