Question 1 (10 points): In the game of Roulette, the probability of a given spin landing on Red is 18/38. What is the probability that over four spins of the Roulette wheel, exactly two spins land on Red? \( \quad \) * Binomial Mandom Variable : \( P(X=x)=\binom{N}{x} P^{x}(1-p)^{N-x} \)

As shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each color is split into two suits of 13 cards each (clubs and spades are black and hearts and diamonds are red). Each suit is split into 13 individual cards (Ace, 2-10, Jack, Queen, and King). If you select a card at random, what is the probability of getting: 1) A(n) 9 of Spade s? 2) A Spade or Heart? 3) A number smaller than 9 (counting the ace as a 1)?

A card is drawn randomly from a standard 52 -card deck. Find the probability of the given event. (a) The card drawn is 5 The probability is : (b) The card drawn is a face card (Jack, Queen, or King) The probability is: (c) The card drawn is not a face card.

A card is drawn randomly from a standard 52-card deck. Find the probability of the given event. (a) The card drawn is 5 The probability is : \( \frac{1}{53} \) (b) The card drawn is a face card (Jack, Queen, or King) The probability is : (c) The card drawn is not a face card. The probability is:

Tickets for a raffle cost \( \$ 11 \). There were 730 tickets sold. One ticket will be randomly selected as the winner, and that person wins \( \$ 1400 \) and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer rounded to two decimal places. Expected Value \( =\$ \$ \)

A jar contains 6 red marbles numbered 1 to 6 and 8 blue marbles numbered 1 to 8 . A marble is drawn at random from the jar. Find the probability of the given event. (a) The marble is red Your answer is: (b) The marble is odd-numbered Your answer is: (c) The marble is red or odd-numbered Your answer is: (d) The marble is blue and even-numbered Your answer is: