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1 year ago

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Suppose James randomly draws a card from a standard deck of 52 cards. He then places it back into the deck and draws a second ca

rd. A standard deck of cards contains four suits: clubs, diamonds, hearts, and spades. There are 13 cards in each suit, which includes three face cards: jack, queen, and king. What is the probability that James draws a queen card as the first card and a diamond card as the second card? Express your answer as a percentage precise to two decimal places.

1 answer:

qwelly [4]1 year ago

7 0

Answer:

1.92%

Step-by-step explanation:

The probability for first case, picking a queen out of deck, will be:

$\frac{4}{52}$

as there will be 4 queens in a deck, one of each suit.

For the second pick, the probability of picking a diamond card, will be:

$\frac{13}{52}$

here the total will remain 52 as he has replaced the first card and not kept it aside and there will be 13 cards in diamond suit (including the three face cards).

Thus the net probability for both cases will be:

$P = \frac{4}{52} * \frac{13}{52}\\ P = \frac{1}{52}\\ P = 0.01923\\P = 1.923\%\\\\P = 1.92\%$

Thus total probability for the combined two cases will be 1.92%

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A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates w

sveta [45]

Answer:

$(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412$

$(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318$

And the 95% confidence interval would be given (-0.1412;-0.0318).

We are confident at 95% that the difference between the two proportions is between $-0.1412 \leq p_A -p_B \leq -0.0318$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion for business

$\hat p_A =\frac{75}{400}=0.1875$ represent the estimated proportion for Business

$n_A=400$ is the sample size required for Business

$p_B$ represent the real population proportion for non Business

$\hat p_B =\frac{137}{500}=0.274$ represent the estimated proportion for non Business

$n_B=500$ is the sample size required for non Business

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412$

$(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318$

And the 95% confidence interval would be given (-0.1412;-0.0318).

We are confident at 95% that the difference between the two proportions is between $-0.1412 \leq p_A -p_B \leq -0.0318$

7 0

1 year ago

The student to faculty ratio at a small college is 17:3 the total number of students and faculty is 740. How many faculty member

larisa86 [58]

Answer:

111

Step-by-step explanation:

It is given that the student to faculty ratio at a small college is 17:3.

Let number of students and faculty members are 17x and 3x respectively.

It is given that total number of students and faculty is 740.

$17x+3x=740$

$20x=740$

Divide both sides by 20.

$x=37$

Number of student $=17\times 37=629$

Number of faculty members $=3\times 37=111$

Therefore, there are 111 faculty members at the college.

3 0

2 years ago

Davi has 75 flower seeds. He wants to plant the seeds in pots so that every seed is planted, and every pot has

Vlada [557]

Answer:

15 pots

Step-by-step explanation:

If you divide 75 by 5 then you get 15. So if you plant 5 seeds per pot then you will need 15 pots to plant all of the seeds.

Hope this is what you wanted.

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2 years ago

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Find the area of the shape shown below.

Liula [17]

Answer:

31.5

Step-by-step explanation:

We can add the areas together

We have a rectangle and a triangle

The area of the rectangle is

A = lw

= 7*3

= 21

The area of the triangle is

A = 1/2 bh

= 1/2 (7)*3

= 21/2

= 10.5

Add them together

A = 21 + 10.5

=31.5

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2 years ago

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Olive oil is a cooking Ingredient. The density of olive oil is 0.92 grams per cubic centimeter. An olive farmer wants to sell bo

sveticcg [70]

Answer: The volume of container that holds 460 grams of oil is 500 cm³.

Step-by-step explanation:

Density of olive oil is $0.92 grams/(centimetre )^3$

An olive farmer wants to sell bottles that contain 460 grams of oil.

Therefore

Mass of oil = 460 grams

As we know

$\text {Density}= \dfrac{\text{Mass}}{\text{Volume}} \\\\\Rightarrow 0.92= \dfrac{460}{\text{Volume}} \\\\\Rightarrow \text{Volume}= \dfrac{460}{0.92} = 500$

Hence, the volume of container that holds 460 grams of oil is 500 cm³.

7 0

2 years ago