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serg [7]
2 years ago
6

Suppose you have a well-shuffled faced-down pile of poker cards: the Ace of Hearts, 2 of Hearts, 3 of Hearts, and 4 of Hearts. Y

ou start picking the cards from the top until both the Ace and the 2 are picked up. What is the expected number of cards you have to pick? (Enter your final answer in decimal format and round to three decimal places.)
Mathematics
1 answer:
Vladimir79 [104]2 years ago
8 0

Answer:

3.5 cards

Step-by-step explanation:

The sample space for picking cards until the A of hearts and the two of hearts are picked up is:

{A,2} {2,A}

{A,1,2} {A,3,2} {A,4,2} {2,1,A} {2,3,A} {A,4,A}

{A,1,3,2} {A,1,4,2} {A,3,1,2} {A,3,4,2} {A,4,1,2} {A,4,3,2}

{2,1,3,A} {2,1,4,A} {2,3,1,A} {2,3,4,A} {2,4,1,A} {2,4,3,A}

There are 20 possible outcomes

The probabilities of needing 2, 3 or 4 cards to draw both the ace and the two of hears are:

P(2)=\frac{2}{20}=\frac{1}{10}\\P(3)=\frac{6}{20} =\frac{3}{10}\\P(4)=\frac{12}{20} =\frac{6}{10}

The expected number of cards needed is:

EV=2*P(2)+3*(P3)+4*P(4)\\EV=0.1*2+0.3*3+0.6*4\\EV=3.5\ cards

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Step-by-step explanation:

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2 years ago
-3y + 8x = 36<br> 6x + y = -21
tiny-mole [99]

Answer:

x=−27/26

and y=−192/13

Step-by-step explanation:

6x+y=−21;8x−3y=36

Step: Solve6x+y=−21for y:

6x+y=−21

6x+y+−6x=−21+−6x(Add -6x to both sides)

y=−6x−21

Step: Substitute−6x−21foryin8x−3y=36:

8x−3y=36

8x−3(−6x−21)=36

26x+63=36(Simplify both sides of the equation)

26x+63+−63=36+−63(Add -63 to both sides)

26x=−27

26x

26

=

−27

26

(Divide both sides by 26)

7 0
2 years ago
2 is subtracted from a number, and then the the difference is multiplied by 5. The result is 30
aev [14]
2 is subtracted from 8 which gives you 6 and 6 times 5 equals 30
6 0
3 years ago
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a random sample of high school seniors were asked whether they were applying for college. the resulting confidence interval for
Artist 52 [7]

Using the confidence interval, the margin of error is 0.02.

In the given equation we have to find the margin of error.

The resulting confidence interval for the proportion of students applying for college is (0.65,0.69).

Let p = population proportion of students applying for college

P = Sample proportion of students applying for college

ME = margin of error

So the confidence interval

CI = (P-ME, P+ME)

From the given question;

(P-ME, P+ME) = (0.65,0.69)

So lower bound= P-ME = 0.65............................(1)

Upper Bound = P+ME = 0.69............................(2)

Simplifying the Equation 1 and 2

Add equation 1 and 2 we get

2P = 1.34

Divide by 2 on both side we get

P = 0.67

Putting the value of P in the equation 2

P+ME = 0.69

0.67+ME=0.69

Subtract 0.67 on both side we get

ME = 0.02

Hence, the margin of error is 0.02.

To learn more about margin of error link is here

brainly.com/question/10501147

#SPJ4

3 0
1 year ago
Can you guys help me finish this quiz tonight
ira [324]

The Answer Is g(x)=1/3x^2

Use (3,3) to find the equation.

3^2x1/3=3

Meaning y or g(x) equals 3. Which is true.

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3 years ago
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