# Work needs to be shown

Please show all work so I can study these problems.

1. Multiplication Probability, basic counting problem. How many seven –digit telephone numbers are there if we cannot have a 1 or 0 in the first place, and no repeats in the last four digits?

2. Simple Probability. The problem will be in the context of a probability experiment. (Size of sample space) n(s), and the size or number of the event space n (E). Then find probability of event E occurring.

Example: When drawing a card at random from a standard deck, what is the probability that you will get a red ace?

3. Additional Rule of Probability. P (E1 or E2), where E1 and E2 are events in the same sample space which may or may not be mutually exclusive. Indicate what n(S) is.

Example: If you draw one card from a deck, what is the probability that you will draw a black ace or a club?

4. Multiplication Rule of Probability. P (E1 or E2), where E1 and E2 form a sequence of events which may or may not be independent. Indicate n(S) is.

Example: Ina shipment of 25 scanners, 5 are defective. If two scanners are selected at random    and tested, find the probability that both are defective (if the first one is not replaced after it has been tested.

1. Simple Probability using a table. If you select a staff member at random, what is the probability of getting a male?

 Staff Females Males Nurses 17 11 Physicians 8 12

E

1. Additional Rule of Probability using a table (using table), If you select a staff member at random, what is the probability of getting a male or a physician?

2. Multiplication Rule of Probability when you make multiple selections (using table), If you select two different staff members at random, what is the probability that they will both be males?

3.

4. Conditional Probability using a table (using table above), calculate with P (E2/E1).

Example: If you select a staff member at random, what is the probability of getting a nurse, given that the staff member is male?

5. Using the Multiplication Rule with Complementary Probability, Independent Events. Complete “at least one” having a certain characteristic.

Example: If you flip a coin 5 times, what is the probability of getting at least one head?

6. Using Multiplication Rule with Complementary Probability, Dependent Events.

Compute at least one certain characteristic, but the events will not be dependent.

Example: If you draw 5 different cards from a deck of cards, what is the probability of getting at least one red cars?

Deck 52 cards, 26 black and 26 red.

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