1.Take simultaneously 4 cards out of a standard deck of 52. Recall that in such a...

1.Take simultaneously 4 cards out of a standard deck of 52. Recall that in such a deck there are exactly 4 Aces and exactly 4 Kings. Let A = At least 2 of the cards taken are Aces and B = At least 2 of the cards taken are Kings.

Referring to the events A and B from the previous question we have:

A A and B are independent

B The contrary of A implies B

C P(A and B)<.1

D A and B are incompatible

Consider a sample space S, a probability P on S, and 7 independent events denoted A^1, A^2, ..., A^7 included in S. Which of the following is NOT true?

A A^1, A^2, A^6 are independent

B The contrary of A^2 and the contrary of A^5 are independent

C A^3, the contrary of A^4 and the contrary of A^7 are pairwise independent

D At least 2 of the 7 given events are incompatible

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Assume that a standard deck of 52 playing cards is randomly shuffled (13 cards of 4...

Assume that a standard deck of 52 playing cards is randomly shuffled (13 cards of 4 types of suits - clubs, diamonds, hearts, and spades). If Alex draws a card from it 4 times with replacement, how many different combinations of suits can he get? (Suppose we further assume that the order doesn't matter: (clubs, diamonds, hearts, hearts) is equal to (hearts, clubs, diamonds, hearts). However, (clubs, diamonds, hearts, hearts) is different with (hearts, clubs, clubs, hearts).)

1. In the game of poker, five cards from a standard deck of 52 cards are...

1. In the game of poker, five cards from a standard deck of 52 cards are dealt to each player. Assume there are four players and the cards are dealt five at a time around the table until all four players have received five cards. a. What is the probability of the first player receiving a royal flush (the ace, king, queen, jack, and 10 of the same suit). b. What is the probability of the second player receiving a...

consider a standard deck of playing cards... 52 cards, 4 suits of 13 cards each, 3...

consider a standard deck of playing cards... 52 cards, 4 suits of 13 cards each, 3 cards of each suit are face cards, 2 suits are black (clubs and spades) and 2 are red (hearts and diamond) a) Let event A be drawing a random card that is a diamond. What is a trial for this scenario? What is the sample space? Is A a simple event? What is P(A)? What is A¯, the complement of A? What is P(A¯)?...

The following question involves a standard deck of 52 playing cards. In such a deck of...

The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...

Hyram has a standard deck of 52 playing cards. The deck contains 4 suits (hearts, diamonds,...

Hyram has a standard deck of 52 playing cards. The deck contains 4 suits (hearts, diamonds, clubs, and spades), and each suit contains 13 cards labeled 2 through 10, as well as jack, queen, king, and ace. Four friends are trying to determine some probabilities related to randomly drawing a single card from the deck. Consider the following events, and then answer the question. A: drawing a diamond B: drawing a queen Which friend provided the correct analysis? Samantha says...

he following question involves a standard deck of 52 playing cards. In such a deck of...

he following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...

Four cards are drawn at random from a standard deck of 52 cards. a. What’s the...

Four cards are drawn at random from a standard deck of 52 cards. a. What’s the probability that at least one card is a 7? b. What’s the probability that 3 of the 4 cards are the same suit? c. What’s the probability that they are all the same suit?

Two cards are drawn at random from a standard deck of 52 cards. The number of...

Two cards are drawn at random from a standard deck of 52 cards. The number of aces drawn is counted. Prepare a probability distribution for this random experiment. Hint: Find the probability that no aces are drawn, exactly one ace is drawn, etc.

Assume that 5 cards are dealt at random from a standard deck of 52 cards (there...

Assume that 5 cards are dealt at random from a standard deck of 52 cards (there are 4 suits in the deck and 13 different values (ranks) per each suit). We refer to these 5 cards as a hand in the rest of this problem. Calculate the probability of each of the following events when dealing a 5-card hand at random. (a) Exactly one pair: This occurs when the cards have numeric values a, a, b, c, d, where a,...

Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously so...

Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously so they are not the same card). There are 12 cards considered face cards. There are 4 cards with the value 10. Let X be the number of face cards in your hand. Let Y be the number of 10's in your hand. Explain why X and Y are dependent.

Subjects