Probability

Probability questions. 3 questions as screenshots. It has probability using formulas and percentages. 3 pictures.

4-letter “words” are formed using the letters A, B, C, D, E, F, G. How many such words are possible for each of the following conditions?
(a) No condition is imposed.
There are
possible “words”.
(b) No letter can be repeated in a word.
There are
possible “words”.
(c) Each word must begin with the letter A.
There are
possible “words”.
(d) The letter C must be at the end.
There are
possible “words”.
(e) The second letter must be a vowel.
There are
possible “words”.
In a certain state’s lottery, 45 balls numbered 1 through 45 are placed in a machine and six of them are drawn at random. If the six numbers drawn match the numbers that a player had chosen, the player wins
$1,000,000. In this lottery, the order in which the numbers are drawn does not matter.
Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.
P(win) =
Preview
A single lottery ticket costs $2. Compute the Expected Value, to the state, if 10,000 lottery tickets are sold. Round your answer to the nearest dollar.
Answer: $
A single lottery ticket costs $2. Compute the Expected Value, to you, if you purchase 10,000 lottery tickets. Round your answer to the nearest dollar.
Answer: S
A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers
in percent form, rounded to 4 decimal places.
Determine the probability that exactly 3 of these cards are Aces.
Answer:
%
Determine the probability that all five of these cards are Spades.
Answer:
%
Determine the probability that exactly 3 of these cards are face cards.
Answer:
%
Determine the probability of selecting exactly 2 Aces and exactly 2 Kings
Answer:
%
Determine the probability of selecting exactly 1 Jack.
Answer:
%