A person in a casino decides to play 3 games of blackjack. Let W denote a win and L denote a loss. Define the event A as “the person wins at least one game of blackjack.” What are the possible outcomes for this event? {WWW, WWL, WLW, WLL, LWW, LWL, LLW} {WWL, LWL, LLW} {W, WW, WWW} {W, LW, LLW} {WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL}

person in a casino decides to play blackjack until he wins a game, but he will not play more than 3 games. Let W denote a win and L denote a loss. What is the sample space for this random experiment? S = {WWW, WWL, WLW, , WLL, LWW, LWL, LLW, LLL} S = {W, WW, WWW} S = {W, LW, LLW} S = {W, LW, LLW, LLL} S = {W, WL, WWL, WWW}

A bookmaker is attempting to calculate the odds of a football team winning the next three matches (match A, match B and match C). They determine the probability of the team winning each respective match to be                P(A) =0.35  ;    P(B) =  0.65 ;   P(C) = 0.58 Assuming that these three events are independent, determine the probability that the team will(i) win all three matches      (Give your answer correct to 3 decimal places)                                                                                    (ii) win at least one match   (Give your answer correct to 3 decimal places)

Jack and Mark are about to play a game with the following rules. They take turns rolling a standard fair die, starting with Jack. The game ends when someone rolls a 1 or 2 or 3 or 4. That person wins the game. Find the probability that Jack will win the game

Three balanced coins are flipped independently. One of the variables of interest is X, thenumber of heads. Let Y denote the amount of money won on a side bet in the followingmanner. If the first head occurs on the first flip, you win $1. If the first head occurs onthe second flip you win $2 and if the first head occurs on the third flip you win $3. Ifno heads appear, you lose $1 (that is, you win −$1).(a) [3 marks] In a table, list all possible outcomes of the experiment, along with thevalues of X and Y associated with each outcome.(b) [3 marks] Determine the bivariate distribution (that is, the joint probability dis-tribution) of X and Y . You can list the probabilities in a table.(c) [3 marks] Find the probability that fewer than three heads will occur and you willwin $1 or less.(d) [2 marks] Are X and Y independent? Why or why no

A game in a casino consists of drawing one card from a standard deck of cards. If the player  Draws an ace, they win €20Draws a face card(Jack, Queen,King) they win €10Draws a 10, they win €5Draws a 2, they lose €5Draws anything else(3 - 9), they win nothingCalculate the expected value of the game (Give your answer correct to 2 decimal places)