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
At a sale, a sofa is being sold for 64% of the regular price. The sale price is $592. What is the regular price?
yulyashka [42]

Answer:

925



Step-by-step explanation:

Formula =592 x 100/64 = 925

8 0
3 years ago
Read 2 more answers
How much does a 5 lb bag for sugar weigh in grams
Mnenie [13.5K]

Answer:

2267.97 grams

Step-by-step explanation:

i hope this helps!

6 0
3 years ago
Read 2 more answers
Evaluate the expression for the given value(s) of the variables s=7 k=4 x=6 8 - k+ x
kow [346]

Answer: 9

Step-by-step explanation:

s = 7

k = 4

x = 6

7 - 4 + 6

3 + 6

9

8 0
2 years ago
A simplified model of the human blood-type system has four blood types: A, B, AB, and O. There are two antigens, anti-A and anti
dexar [7]

Answer: Blood type will be A when event "A" happened and event "B" did not happen. Blood type will be B when event "A" did not happened and event "B" happened. Blood type will be AB when both events happened and blood type will be O when both events did not happen.

Step-by-step explanation:

S={AntiA reacts; AntiA does not react; AntiB reacts; AntiB does not react}

If AntiA reacts and AntiB reacts = AB (A∩B)

If AntiA does not react and AntiB does not react= O (A'∩B')

If AntiA reacts and AntiB does not react= A (A∩B')

If AntiA does not react and AntiB reacts= B (A'∩B)

4 0
3 years ago
Jane has 15 coins in total of $2.18. She has 5 more quarters than nickels, has 3 pennies and dimes. How many quarters, nickels,
fredd [130]
She has 7 quarters two nickels and 3 dimes
8 0
3 years ago
Other questions:
  • Sam recorded how many punded he gained each month for four months and recorded the results as: 1/8, 0.75, 2/5, 5,6. list the amo
    10·1 answer
  • 4/9 divided by ? equals 12
    5·1 answer
  • Sum is 45 and the difference is 5 what are the two numbers
    13·1 answer
  • Denote by SS the set of integers {−44,−43,...,−38−44,−43,...,−38}. Count the number of BIJECTIVE functions φ:S→Sφ:S→S such that
    6·1 answer
  • Congruen Figures lyures Which figure is congruent to the given figure? Will give brainliest ​
    12·1 answer
  • Write the equation whose roots are 6 and 1, and whose leading coefficient is 4.
    15·1 answer
  • Which expression is equivalent to one over four n − 16? (4 points)
    11·2 answers
  • Can somebody help me plss
    5·1 answer
  • GUYS PLEASE HELP ME
    6·2 answers
  • Please answer who ever answers first and correct will get brainliest
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!