A regular poker hand is drawn from a well-shuffled deck of cards. What is the pr
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Question
A regular poker hand is drawn from a well-shuffled deck of cards. What is the probability that it will be a two-pair hand? What is the probability that it will be a straight Bush hand? What is the probability that it will be a straight hand? A deck for Number Skat consists of the cards in a regular Poker deck, but all Jacks, Queens and Kings are taken out. Consider the random experiment of drawing one card from a well-shuffled deck for Number Skat. What is the size of the sample space? Consider the event E of drawing an Ace, a Two or a Three, all black, from a well-shuffled deck for Number Skat (spades and clubs are black; hearts and diamonds are red). How many outcomes are there in event E? What is the probability of E? What is the probability of not drawing a black card which is an Ace, a Two or a Three? A student is taking a multiple-choice quiz. The quiz has 6 questions, Consider the random experiment "Roll two identical dice and observe the difference". Find the sample space. Assuming the dice are fair, find the probability space. (Hint: use the diagonals in Figure 3.1.) Two distinguishable dice are rolled and the numbers on top are observed. Consider the event E: "one of the numbers is twice the other" Write E as as set of outcomes. b) If the the two dice are fair, what is the probability of E? Refer to Exercise 29. What is the probability of E if the first die is fair and the second die has probability distribution given by. die of Example 3.2.2, and the coin is fair. Given that a 7-digit phone number cannot start with 0 or 1 find the following: The number of all possible phone numbers in a given area code. The number of all such phone numbers with no repeating digits. The number of all such phone numbers with at least one repeating digit. The probability of having a phone number with no repeating digits and the probability of having a phone number with at least one repeating digit.Explanation / Answer
Example:
a) All poker hands: C(52,5) = 2,598,960 hands
Now you throw all the diamonds and hearts away, keep 26 cards in hands and draw 5 cards: C(26,5) = 65,780 hands.
Probability: 65,780/2,598,960 ? 2.531%
Your logic was flawed like this: You supposed that red and black cards play equally important roles, but the presence of just ONE red card will totally render the hand unacceptable, so even if 1 red card is present, there's a chance (although small) it will be dealt, ruining your hand's legitimacy.
ADDITIONAL SOLUTION:
First card being black: 26/52 chance
2nd card......................: 25/51 chance
3rd................................: 24/50 chance
4th.................................: 23/49 chance
5th.................................: 22/48 chance
=> 253/9996 ? 2.531%
b) Since it has only black cards, there's only 2 ace in 26 cards:
Total hands that can be dealt: 26C5 = 65,780
Now you discard 2 aces and deal a hand with 24 cards: 24C5 = 42,504
=> Hands with 1 or 2 aces: 65,780 - 42,504 = 23,276 hands.
Probability: 23,276/2,598,960 ? 0.0896%
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