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balandron [24]
3 years ago
8

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a spade fo

r the second card drawn, if the first card, drawn without replacement, was a heart? Express your answer as a fraction or a decimal number rounded to four decimal places
Mathematics
1 answer:
Gre4nikov [31]3 years ago
8 0

Answer: 0.5049

Step-by-step explanation:

The probability that the first card drawn is a heart is 13/52 = 1/4

The probability that the second card drawn, without replacement, is a spade is 13/51

So the probability of drawing a heart for the first card and spade for the second card is

1/4 + 13/51 = 103 / 204 = 0 5049

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kiruha [24]
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3 years ago
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jekas [21]
The mode is 44
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3 years ago
(a) Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the prop
zalisa [80]

Answer:

(a) The sample sizes are 6787.

(b) The sample sizes are 6666.

Step-by-step explanation:

(a)

The information provided is:

Confidence level = 98%

MOE = 0.02

n₁ = n₂ = n

\hat p_{1} = \hat p_{2} = \hat p = 0.50\ (\text{Assume})

Compute the sample sizes as follows:

MOE=z_{\alpha/2}\times\sqrt{\frac{2\times\hat p(1-\hat p)}{n}

       n=\frac{2\times\hat p(1-\hat p)\times (z_{\alpha/2})^{2}}{MOE^{2}}

          =\frac{2\times0.50(1-0.50)\times (2.33)^{2}}{0.02^{2}}\\\\=6786.125\\\\\approx 6787

Thus, the sample sizes are 6787.

(b)

Now it is provided that:

\hat p_{1}=0.45\\\hat p_{2}=0.58

Compute the sample size as follows:

MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}

       n=\frac{(z_{\alpha/2})^{2}\times [\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})]}{MOE^{2}}

          =\frac{2.33^{2}\times [0.45(1-0.45)+0.58(1-0.58)]}{0.02^{2}}\\\\=6665.331975\\\\\approx 6666

Thus, the sample sizes are 6666.

7 0
3 years ago
5/6+2i<br><br><br>Aka<br><br><br> 5<br><br>___<br><br>6+2y<br>Ignore my answer its probably wrong
liberstina [14]

Answer:

   (3/4) -(1/4)i

Step-by-step explanation:

Your answer is correct.

\dfrac{5}{6+2i}=\dfrac{5(3-i)}{2(3+i)(3-i)}=\dfrac{5(3-i)}{2(9+1)}\\\\=\dfrac{3-i}{4}=\dfrac{3}{4}-\dfrac{1}{4}i

8 0
3 years ago
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Subtract 6 from the x value in the first one, and remember that slope intercept form is mx+b
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