A fair die is rolled in a board game to determine how many spaces a player can move on their turn. It has one of the numbers 1,2,3,4,5, or 6 on each of its faces.
Let event A be rolling an even number and event B be rolling an odd number.
Identify the numbers of each of the following:
Provide your answer below:
There are _______ outcomes in the sample space.
There are _______ outcomes in event A.
P(A)=_______ is the probability that you choose an even number.
A fair die is rolled in a board game to determine how many spaces a player...
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.What is P(A), the probability that the six-sided die is an even number?What is P(B), the probability that the four-sided die is an odd number?What is P(A...
Suppose a casino has a game where a fair six-sided die is rolled. If an odd number is rolled, the player loses $2. If a six is rolled, the player wins $20. Otherwise, the player loses $1. If a player played this game 1000 times, how much money should he expect to gain (or lose)? Show work.
This question is due my 11:50pm EST One die is rolled 2 times in a row. The observation is the number that comes up on each roll (rolling 2 and 5 is not the same as rolling 5 and 2). Describe one outcome and find a number of outcomes. Write all outcomes of the sample space S (you can use … notation to indicate many numbers of cases). : “pairs are rolled” (both dice come up the same number) Write...
Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is allowed to bet on two sets of outcomes: A (1,2,3) and B (2,4,5,6). If he bets on A then he wins $1 if one of the numbers in A is rolled and otherwise he loses $1 -let X be the amount won by betting on A (so P(X-1)-P(X1)If he bets on B then he wins $0.50 if a number in...
Three six-sided fair dice are rolled. The six sides are numbered 1,2,3,4,5,6. Let A be the event that the first die shows an even number, let B be the event that the second die shows an even number, and let C be the event that the third die shows an even number. Express each of the following events in terms of the named events described above: 1) the event that all three dice show even numbers 2) the event that...
"Chutes and Ladders" is a popular board game for children. The game consists of a board that has squares which are numbered from 1 to 100, and players have counters which start on the theoretical square 0. On each player’s turn, the player generates a random integer number from 1 to 6 (e.g. by rolling a die or spinning a wheel) and move their marker through the board that many spaces. If you land at the bottom of a ladder...
A fair, six-sided die is rolled. Describe the sample space S, identify each of the following events with a subset of S and compute its probability (an outcome is the number of dots that show up). a. Event T = the outcome is three. b. Event A = the outcome is an odd number c. Event B = the outcome is less than four. d. Event D = the complement of A e. A AND B f. A OR B...
Two coins are flipped and a die is rolled. (a) Write the sample space for this experiment. (b) Let A be the event that both coins will be heads. Write the outcomes in A. (c) Let B be the event that result of the dice roll will be an odd number. Write the outcomes in B.
1. Consider a fair four-sided die, with sides 1, 2, 3, and 4, that is rolled twice. For example, "1,4" would indicate 1 was rolled first and then 4 was rolled second a) Write down the possible outcomes, i.e., the sample space. (b) List the outcomes in the following events: Event A: The number 4 came up zero times. Event B: The number 4 came up exactly one time. . Event C: The sum of the two rolls is odd...