You have a standard deck of cards. You divide this deck in half by selecting uniformly at random 26 of the deck’s 52 cards and placing them in your left hand. You hold the remaining 26 cards in your right hand. Prove that the expected number of aces in your right hand is 2.

Q: Sarah is about to draw a card at random from a standard deck of 52 playing cards. If he draws a…

A:

Q: A committee of 3 people is to be randomly selected from a group of 8 people, including Sarah.…

A: To Determine: The probability that Sarah is selected to be on the three-person committee.

Q: Assume that you select 4 coins at random from 11 coins: 5 dimes and 6 quarters. What is the…

A: It is been asked to find the probability that all of the coins selected are dimes using the given…

Q: Denni has 15 coins in his pocket, and 6 of them are toonies. He reaches into his pocket and pulls…

A:

Q: A monkey is given 12 blocks: 3 shaped like squares, 3 like rectangles, 3 like triangles, and 3 like…

A: Total blocks = 12  Square = 3  Rectangle = 3  Triangle = 3  Circles= 3  Order matters  If it draws…

Q: Assume that you select 2 coins at random from 8 coins: 3 dimes and 5 quarters. What is the…

A:

Q: A box contains 3 pink balls, 8 yellow balls, and 9 white balls. A first ball is selected, and then…

A:

Q: Two cards are drawn at random from an ordinary deck of 52 cards. Find the probability that the…

A: The provided information is There are 52 cards of deck. We find the probability the 2-card hand…

Q: If the probability of Ali and Hamad winning in a competition is 0.37 and the probability of losing…

A: It is given that the   probability of Ali and Hamad winning in a competition is 0.37 i.e. P(Ali and…

Q: Ruben is packing school lunches for his two daughters. In his fruit bowl, he has 4 red apples, 2…

A: Given that, Ruben is packing school lunches for his two daughters. In his fruit bowl, he has 4 red…

Q: what is the probability that 2 will have no checkup, 3 will have 1 checkup, and 2 will have 2…

A: The probability that a person will have 0, 1, or 2 dental checkups a year is 0.24, 0.51, and 0.25…

Q: Suppose you have 10 tennis balls and you randomly pick some number of them. What is the probability…

A: Given the event that there are 10 tennis balls and one randomly pick some number of them.

Q: You are dealt a hand of 13 cards, find the probability that you have 4 hearts, 3 spades, 5 diamonds…

A: Given that  Total number of cards=52 Number of hearts cards=13 Number of spades cards=13 Number of…

Q: The probability of being dealt a hand containing 3 spades, 4 hearts, 2 diamonds, and 2 clubs is.…

A: Here use hypergeometric distribution

Q: Three people are selected randomly from a group consisting of 5 parents and 9 children. Find the…

A: Ans# - Given three people are selected randomly from a group consisting of 5 parents and 9 children.…

Q: In a card game, there are 15 cards laid out on a table. 6 of the cards are blank, 2 of the cards are…

A: Here, we use the expected value and probabilty for the purpose of knowing the variables probability…

Q: A manufacturing company uses an acceptance scheme on items from a production line before they are…

A: Note: As per our guidelines we are supposed to answer only one question per post so i am solving…

Q: Find the probability that you will draw the 2 of diamonds first, 6 of hearts second, ace of spades…

A: The number of cards in a deck of cards is 52.

Q: Meredith draws a six from a standard deck of 52 cards. Without replacing the first card, she then…

A:

Q: Find the probability of winning second prize—that is, picking five of the six winning numbers—with a…

A: We can select any 6 numbers from 54 numbers in 54C6 ways. (this is the total number of ways)   We…

Q: Steve has 12 biscuits in a tin. There are 5 digestive and 7 chocolate biscuits. Steve takes two…

A: Given that, Total number of biscuits = 12 5 digestive biscuits and 7 chocolate biscuits We to find…

Q: In a drawer, there are 13 pairs of socks, 10 of which are white, and 8 t-shirts, 5 of which are…

A: Here in a drawer there are 13 pairs of shock from which 10 are white. 8 t-shirts from which 5 are…

Q: A drunken man who has n keys wants to open the door if his office. He tries the keys at random, one…

A: Given The total number of keys =n The unsuccessful keys are eliminated and one by one keys are tried…

Q: Three cards are selected at random from the standard pack of 52 cards. Find the probability that 2…

A: Solution-: We find probability that 2 jacks when 3 cards are selected at random from the standard…

Q: In a poker hand consisting of 5 cards, find the probability of holding (a) 3 jacks; (b) 3 clubs and…

A: Given that ,In a poker hand consisting of 5 cards .We have to find the probability of holding(a) 3…

Q: Assume that you randomly pick one of the bowls: X, Y, or Z. You then randomly draw one ball out of…

A: Let us denote R=Red, W=white, B=blue   There are 3 bowls So, P(X)=13, P(Y)=13, P(Z)=13P(B or…

Q: It costs $6.75 to play a very simple game, in which a dealer gives you one card from a deck of 52…

A: The cost of the game is $6.75.

Q: You are dealt one card from a 52-card deck. Find the probability that you are dealt a red 7 or a…

A: Given: Number of cards in a deck = 52 Number of 7 red = 2  Number of 8 black = 2

Q: From a group of 10 choldren, a team of 5 (the red team) is randomly chosen. The remaining 5 children…

A: Given from a group of 10 children, a team of 5 children is randomly chosen. The remaining 5 children…