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Kryger [21]
2 years ago
13

If you draw four cards at random from a standard deck of 52 cards, what is the probability that all 4 cards have distinct charac

ters (letters or numbers)
Mathematics
1 answer:
mezya [45]2 years ago
4 0

There are \binom{52}4 ways of drawing a 4-card hand, where

\dbinom nk = \dfrac{n!}{k!(n-k)!}

is the so-called binomial coefficient.

There are 13 different card values, of which we want the hand to represent 4 values, so there are \binom{13}4 ways of meeting this requirement.

For each card value, there are 4 choices of suit, of which we only pick 1, so there are \binom41 ways of picking a card of any given value. We draw 4 cards from the deck, so there are \binom41^4 possible hands in which each card has a different value.

Then there are \binom{13}4 \binom41^4 total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is

\dfrac{\dbinom{13}4 \dbinom41^4}{\dbinom{52}4} = \boxed{\dfrac{2816}{4165}} \approx 0.6761

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An Ontario lottery has the following structure, the first person drawn from the names wins $15 000. Each subsequent person drawn
elixir [45]
  • The first four terms are : 15000, 14850, 14700, 14550
  • a = 15000 ; d = -150
  • The explicit formula is : a_{n} =  - 150n \:  + 15150

The first term of the sequence, a = 15,000

Each subsequent winner gets $150 less

Hence, the common difference, d = - $150

The first four terms :

First term, a1 = $15000

Second term, a2 = a - d = $15000 - $150 = $14850

Third term, a3 = a2 - d = $14850 - $150 = $14700

Fourth term, a4 = a3 - d = $14700 - $150 = $14550

a, for the sequence is the first term = $15000

d, for the sequence is the common $150 (difference between successive wins).

Explicit formula for the general term :

a_{n} \:  = nd \: + c

For n = 1

15000 = 1( - 150)  + c

15000 =  - 150 + c

c = 15150

Hence, the explicit formula for the nth term is :

a_{n} \:  =  - 150n \:  + 15150

Learn more : brainly.com/question/12006170

3 0
3 years ago
Liz got home from school at 4:33. She decided to bake muffins as an after-school snack. It took Liz 55 minutes to prepare and ba
IgorC [24]

Answer:

The muffins were done at 5:28

Step-by-step explanation:

you add 4:33 to 55 minutes knowing well that 60mins makes one hour

4:33

55

5:28

6 0
2 years ago
On Monday morning the temperature was 38°F, but by the afternoon the temperature had risen 22°F. On Tuesday morning the temperat
Anika [276]
The temperature on Tuesday afternoon is below 38 degrees Fahrenheit. As it states in the question the temperature on Tuesday morning was 27 degrees Fahrenheit and rose 10 more degrees at noon. Which makes is 37 degrees Fahrenheit at noon on Tuesday. You get this by taking 27 degrees and adding 10 degrees.  
7 0
3 years ago
Read 2 more answers
Please help!!
inessss [21]

Answer:

2.82 seconds (3 sf)

Step-by-step explanation:

s = ut + 0.5at²

6 = -95(sin25)t + 0.5(32)t²

16t² - 40.14873487t - 6 = 0

t = 2.818501699, -0.1419193751

t is time so can't be negative.

Therefore, t = 2.82s (3 sf)

4 0
3 years ago
Sasha performs an experiment. She chooses one marble from each of three sacks. The first sack has black (B) and white (W) marble
Paladinen [302]

Answer:

Option D is correct

Step-by-step explanation:

From the question, we have:

Sack\ 1: B, W

Sack\ 2: G, Y

Sack\ 3: S, R

Required

The tree diagram

The selection process is as follows:

Sack\ 1: B, W

Sack\ 1\ and\ Sack\ 2: B (G,Y); W(G,Y) -- i.e. we write sack 2 as a subset of 1

Sack\ 1, 2\ and\ 3: B (G(S,R),Y(S,R)); W(G(S,R),Y(S,R)) -- i.e. we write sack 3 as a subset of 2

<em>The only tree diagram that illustrates this is: option D</em>

5 0
3 years ago
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