# What is the probability that both cards are of the same suit?

## What is the probability that both cards are of the same suit?

So is the probability to get two cards of any other suit. Thus the total probability to get two cards of the same suit is 4*1/17=4/17.

**What is the probability of getting a full house in a 5 card poker hand?**

Frequency of 5-card poker handsHandDistinct handsProbabilityFull house1560.1441%Flush (excluding royal flush and straight flush)1,2770.1965%Straight (excluding royal flush and straight flush)100.3925%Three of a kind8582.1128%7

**What is the probability that a 5 card poker hand contains at least one diamond?**

The probability of getting at least one diamond = 1-P(no diamonds).

### What is the probability of drawing at least one ace?

75 (3/4). The chance of drawing one of the four aces from a standard deck of 52 cards is 4/52. Thus, the chance of drawing at least one ace in two draws is 4/52 + 4/52 – (4/52 × 3/51), or 33/221.

**What is the probability that a 5 card poker hand has at least one ace?**

Then the solution to the problem – that is, the probability of at least one ace appearing in a 5-card hand – is one minus the complement: 1−(485)(525).

**What is the probability that a bridge hand will contain at least one ace?**

There is a 44% chance of getting exactly one ace.

#### What is the probability of getting at at least one ace and at least one king in a poker hand of five cards dealt from 52 cards?

This is equal to the number of ways of selecting no kings. So we have: C525−2C485+C445 ways of selecting 5 cards from a deck such that we have at least one ace and at least one king. The probability of this is then C525−2C485+C.

**What is the probability that we draw 2 aces and 3 kings?**

3! 2! =10 ways to order “AAAKK” so the probability of “3 aces and 2 kings” drawn from a 54 card deck is 10(4/54)(3/53)(2/52)(4/51)(3/50).

**What is the probability that a randomly selected poker hand contains exactly 3 aces given that it contains atleast two aces?**

There are 2,598,960 five card poker hands. 1,712,304 have no Aces, 778,320 have one Aces, 103,776 have two Aces, 4,512 have three Aces and 48 have four Aces. Therefore 108,336 hands have at least two Aces, so the probability you are asking for is or or about 4.16%.

## What is the probability of drawing 3 face cards in a row?

100%

**How many 5 card poker hands with all spades are possible?**

All 5 cards are from the same suit and they form a straight (they may also be a royal flush). The number of such hands is 4*10, and the probability is 0.

**How many different 5 card hands can be dealt from a deck of 52 cards if the hand consists of exactly 2 aces?**

10 possible

### How many different ways can you pick 3 aces in a 7 card hand?

There are 3! ways to distribute aces into the first 3 slots. And then there are (494) ways to fill the remaining slots.

**How many ways can 3 cards be selected from a 52 card deck?**

To answer a), we note that there 52 ways to choose the first card, 51 ways to choose the second card, and 50 ways to choose the third card, for a total of 132,600 ways. More generally, there are n!/(n-k)! ways to choose ordered k-element subsets from an n-element set. These are called permutations.

**How many ways can cards be selected from a 52 card deck?**

So, by using the Counting Principal, we have 52*51 = 2652 ways to draw two cards from a deck of 52 without replacing the first card before drawing the second card.

#### How many ways can 4 cards be selected from a 52 card deck?

SOLUTION: For hands of cards, unless we are told otherwise, the cards dealt must be different, and the order in which they are dealt does not matter. So, we are counting the number of combinations of 4 cards chosen from 52, which gives 52C4=52P4 / 4! =(49) / (4Χ3Χ2Χ1) =6,497,400 / 24 = 270,725 hands.