Please answer the question clearly
Please answer the question clearly 10. If two cards are randomly drawn (without replacement) from an...
Two cards are randomly drawn (without replacement) from an ordinary deck of 52 play- ing cards. Let W be the number of aces obtained in the first draw, and Z be the number of pairs obtained in the two draws. a) Find the joint probability mass function of W and Z b) Are W and Z independent? Please justify your answer.
Draw three cards without replacement from a deck of cards. Let H be the number of hearts and S the number of spades drawn. (a) Find the joint pmf of (H, S) (b) Find P(H = S)
Three cards are randomly selected from a fair deck (without replacement). Find the probabilities of the following events by applying the definition of conditional probability: • All hearts, given all cards are red. • All hearts, given one of the cards is a king • All hearts, given no spades. • All hears, given two kings.
Assume that you are asked to select three cards without replacement from the 39 cards that contain the hearts, diamonds, and clubs from an ordinary deck of 52 playing cards. Let X be the number of clubs selected and Y the number of diamonds. (a) Find the joint probability distribution of X and Y. (b) Find P[(X,Y)EA), where A is the region given by {(x,y) | X + y2 2} (a) Complete the joint probability distribution below. (Type integers or...
Two cards are drawn without replacement from an ordinary deck, find the probability that the second is a heart, given that the first is a heart.What is the conditional probability?Thank you.
probability, show all work 7. Let 3 cards be taken at random and without replacement from an ordinary deck of cards. Let X be the number of spades and Y be the number of hearts. Find (1) pmf of X (2) Joint pmf of X and Y. (3) P(X 2,Y 1). (10 Points)
3. A hand of five cards is drawn simultaneously (without order or replacement) from a standard 52-card deck. Let A be the event that the hand includes four cards of the same kind, and let B be the event that at least two of the cards in the hand are of the same kind. a. Compute P(A) (5) b. Compute P(B). (5) c. Compute P(AB) (5) 4. Suppose Z and X are continuous random variables such that Z has a...
8. Assume three cards are drawn from a standard 52-card deck without replacement. Answer each of the following questions. a) What is the probability that the third card will be the two of clubs? b) Are your odds better for choosing the two of clubs on your first, second, or third draw? c) How can you use this example to illustrate the difference between independent and dependent events? d) How do the marginal, joint, and conditional probabilities change if we...
Two cards are drawn without replacement from an ordinary deck, find the probability that the second is a ten, given that the first is a ten. What is the conditional probability? (Type an integer or a simplified fraction.) Enter your answer in the answer box
please make answer clear for a thumbs up:) A card is randomly drawn from a deck of well-shuffled playing cards. Let event be that the card is a jack and event F be that the card is a heart. A standard 52 card deck is split ovenly into four suits of cards (heart diamonds, clubs, and spades). Each suit contains the cards ac,2,310, jack, goon, king a) Find PE) and P(E) b) Find PF) and P(F) c) Find PEUF)