1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
marta [7]
3 years ago
10

A poker hand is a set of 5 cards randomly chosen from a deck of 52 cards. Find the probability of a (a) royal flush (ten, jack,

queen, king, ace in a single suit). (b) straight flush (five in a sequence in a single suit, but not a royal flush). (c) four of a kind (four cards of the same face value). (d) full house (one pair and one triple, each of the same face value). (e) flush (five cards in a single suit but not a straight or royal flush). (f) straight (five cards in a sequence, not all the same suit). (Note that in straights, an ace counts high or low.) g
Mathematics
1 answer:
zysi [14]3 years ago
5 0

Answer:

a) 0.000001539

b) 0.00001385

c) 0.0002401

d) 0.001441

e) 0.001966

Step-by-step explanation:

Since there are 52 deck of cards, and the hand of the poker is 5 set, then the total number of hands achievable would be

T = 52! / 5!(52 - 5)!

T = 52! / 5! 47 !

T = 2598560 possibilities.

a) There are 4 ways of getting a royal flush. So the probability of getting a royal flush is

4 / 2598560 =

0.000001539

b) There are 9 hands from the 5 card hands, and also, there are 4 possible suits. So then, the probability is

9 * 4 / 2598560 =

36 / 2598560 =

0.00001385

c) There are 13 possible ways to get a four of a kind, since there are 5 cards with the poker, the remaining would be taken from the 48 remaining cards, thus

13 * 48 / 2598560 =

624 / 2598560 =

0.0002401

d) 3 of a kind in conjunction with a pair is needed to form a full house. This 3 of a kind can be gotten from any 4 suits. Then again, the pair has two cards with the same face value. So,

4! / 2! (4 - 2)! =

4! / 2! 2! = 6

That means, there are 6 possible ways to get our needed suits. Then, the probability of getting a full house is

13 * 4 * 12 * 6 / 2598560 =

3744 / 2598560 =

0.001441

e) To get a flush, all the 5 cards in the hand needs to have the same suit. Now, there are 13 different types of cards with only 5 cards being in the hand, thus

13! / 5! (13 - 5)! =

13! / 5! 8! = 1287

Now, recall that the question specifically asked us not to include any straight. There are 10 straights that can be gotten, and thus, we subtract it.

1287 - 10 = 1277

Since there are 4 suits, the probability of getting a flush is

1277 * 4 / 2598560 =

5108 / 2598560 = 0.001966

You might be interested in
Is ABD = CDB?? Justify the answer I will mark the brainiest :))
mel-nik [20]
Yes ABD=CBD since they both are just half of the triangle
3 0
2 years ago
Read 2 more answers
Which vocabulary word best describes the math sentence you see here?
nlexa [21]

Answer:

Expression

Step-by-step explanation:

Remember, an expression is a mathematical phrase that contains numbers, variables, or both. Expressions never have an equal sign. An equation is a mathematical sentence that says two expressions are equal. My work don't copy®️

7 0
1 year ago
Subtract the following:<br> –7 – 7=<br> 7 –<br> 7=<br> -7-(- 7) =<br> 7- (-7)=
Ratling [72]

Answer:

A. -7 - 7 = -14

B. 7 - 7 = 0

C. -7 - (-7) = 0

D. 7 - (-7) = 14

5 0
3 years ago
Read 2 more answers
What is the product?<br><br> Enter your simplified answer in the box.<br> −14⋅(−611)−14⋅(−611)
allochka39001 [22]
The answer i got is 17108.
8 0
3 years ago
Read 2 more answers
Helpppp please ASAP
Molodets [167]

Answer:

I got 12√ 2  

PLZ CORRECT ME IF I AM WRONG PLZ AND THXS YOU

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Geometry help????????
    6·1 answer
  • The local bike shop sells a bike and accessories package for $276. If the bike is worth 5 times more than the accessories, how m
    15·1 answer
  • Plan g is paid 14,000 for a concert. If the money made is split at 2:5 between plan g and the arena. How much money did the aren
    11·1 answer
  • Just number 23 super confused
    13·1 answer
  • Can someone please help i have until 12am which is 45 minutes away for me!!
    10·1 answer
  • Find the next term of the sequence.<br> 24, 17, 10, 3, ...<br><br> -7 <br> 0<br> -4<br> -5
    9·1 answer
  • Look the image below
    5·2 answers
  • Dollhouse furnishing comes in different sizes depending on the size of the dollhouse. Write a ratio of the size of the dollhouse
    5·1 answer
  • Mr. Chavez needs 7 lbs of gummy bears to make gummy bears with chamoy
    15·1 answer
  • Calculate the area of a triangle with a base of 6 cm and a height of 12 cm
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!