Example 3-22. If 6n tickets numbered 0, 1, 2, ..., 6n – 1 are placed in a bag and three are drawn out, show that the chance that the sum of the numbers on them is equal to 6n is 3n(6n - 1) (6n – 2).

Q: A box contains 20 balls, of which 10 are red and 10 are blue. We draw ten balls from the box, and we…

A: Given: Total number of balls = 20 Number of red balls = 10 Number of blue balls = 10

Q: What chance do you have of winning the lottery if there are 1 million entries and each of you have…

A: If the probability of getting selected for each outcome is equal then such outcomes can be termed as…

Q: Q5. A box contains 20 balls, of which 10 are red and 10 are blue. We draw ten balls from the box,…

A: 10 red10 blue20 totalselect 10 ballswe want to find probability that exactly5 are red and 5 are blue…

Q: 5. The probability that at least one of the events A and B will occur is P(A ∪ B) = P(A) + P(B) −…

A: and

Q: A game that draws 5 digits from 1-49 from the same machine. In other words, numbers are drawn and…

A:

Q: We have an empty 4X4 grid. We then place 4 apples at random in different squares of the grid. What…

A: Let us represent 4X4 grid by coordinates (i,j) where, i =1,2,3,4 and j = 1,2,3,4 So, there are 4*4 =…

Q: A casino offers the following game, which costs 10 dollars to play. Two cards are selected at…

A: Considering the provided information, if both of the cards are kings, then you win = 220+10-10 =…

Q: Ed and Taylor work together on a group quiz that has 15 multiple-choice questions, each with 4…

A: It is given that Ed and Taylor work together on a group quiz that has 15 multiple-choice questions,…

Q: you roll two fair dice. How many ways are there for the sum of the dice to be less than 6?

A: On rolling two dice, let X be the sum of the outcomes. The all possible values of X is…

Q: One of two urns is chosen at random with one as likely to be chosen as the other. Then a ball is…

A: Number of balls in first urn = 1 white and 5 red ballsNumber of balls in second urn = 4 white and 2…

Q: Two boxes A and BA contains 2 red and 6 white balls and B contains 2 red and 1 white balls. If one…

A:

Q: Suppose that 12% of the families in a certain community have no children, 22% have one, 34% have…

A: Answer:- According to the given information,  P( no children) = 12% = 0.1200  P( one children) = 22%…

Q: A committee of 5 persons is to be selected randomly from a group of 5 men and 10 women. (a) Find the…

A: Given that there are 5 men and 10 women. So total (5+10)=15 people.   We can select any 5 people in…

Q: A box contains 20 balls, of which 10 are red and 10 are blue. We draw ten balls from the box, and…

A:

Q: A die is rolled. If an odd number turns up, we win an amount equal to this number; if an even number…

A: The outcome of rolling a die is {1, 2, 3, 4, 5, 6}.

Q: Suppose a family consisting of a father and a son plays a "Gambler's ruin" game for the Chinese New…

A: Let:q be the probability of the father winning a token.p be the probability of the son winning a…

Q: A magician's hat contains black rabbits and white rabbits. The magician selects two rabbits without…

A:

Q: A number is drawn at ramdom from a box. There is a 20% chance for it to be less than 10. There is…

A: A number is drawn at ramdom from a box. There is a 20% chance for it to be less than 10. There is…

Q: 8 For this problem, assume there are 3 grey females, 4 grey males, 2 white females, and 3 white…

A:

Q: Suppose you are playing a game of Yahtzee. You know that you play with 5 dice, each with 6 sides.…

A: Imagine that you are engaged in a game of Yahtzee. You are aware that there are five dice in use,…

Q: If someone were to bet $1 on the second dozen numbers (which pays 2 to 1) in the game of roulette 33…

A: Introduction: Denote X as the random variable representing the number of separate times the player…