Question

fine the probability of dealing a five-card hand that contains the ace, king, queen, jack and ten of the same suit from a deck of 52 cards

Answer 1

Pretty darn small :-)

Answer 2

There's four ways this can happen: all hearts/spades/clubs/diamonds

Total number of possible 5 card hands is (from 52 cards, choose 5): 52C5 = 2598960

There are only four possible desirable outcomes: AKQJT hearts, AKQJT diamonds, AKQJT spades, AKQJT clubs.

Probability = # desired outcomes/total possible outcomes.

Answer 3

the answer is its 1/649740

Answer 4

Try what I gave you and simplify the fraction.

Answer 5

\[P = \frac{ 4 }{ 2598960} = ? \]

Answer 6

how u come with 4? how u get that?

Answer 7

Read what I wrote above again.

Answer 8

yeah oi got it thanks!

Answer 9

\[52C5 = \frac{52!}{(52-5)! 5!} = \frac{52*51*50*49*48 }{5*4*3*2*1} = 2598960\]

Answer 10

Now you know you odds of being dealt a royal flush (in 5 card draw) :)

Answer 11

Lesson: if you want a royal flush, bring a few extra cards ;-)

Answer 12

haha. Well it's more likely in texas hold 'em, I think I've hit 3ish playing hold 'em.

Answer 13

how many decks were in play?

Answer 14

One... why would you play with more than one deck?

Answer 15

I should note that I've played several hundred thousand hands of hold 'em :P

Answer 16

I just checked, and I have 3 royal flushes, and 11 more straight flushes, out of 597,000 hands.

Answer 17

Here is an interesting way to think of probability,
what is the chance that a head will turn up after two flips of a coin?

Answer 18

I'm guessing you mean what's the chance of getting a head on the 2nd flip... 50%.

What's the chance of getting a head on the 10th flip, if the previous nine flips were heads?

Answer 19

What's the total chance that a head will turn up either on the first flip or the second flip?

Answer 20

If you mean an exclusive 'or' ie not allowing HH, then 50%. 75% with an inclusive 'or':

HH, HT, TH = 3 desired outcomes

HH, TT, HT, TH = 4 total possible outcomes

Answer 21

I think you meant an exclusive or, that's usually the standard in maths. So 50%.

Answer 22

I meant the inclusive or, because that gives the strange result.

Answer 23

But it's not too strange if you think of it as "if you toss two coins, what's the chance of getting at least one head". The probability of at least one head will of course increase with the number of coin tosses. eg if you tossed a coin 10 times, the chance of zero heads coming up is 0.5^10.

Answer 24

You're right! The strangeness is gone if you think of it as tossing two coins once :)

Answer 25

Or if you think of it as very many coin tosses. If you toss a coin 100 times, you'd expect to see a few heads show up!