Please help with similarity

Michelle draws a card from a standard deck of 52 cards. She replaces the card and draws a second card. What is the probability t

erma4kov [3.2K]

To draw a heart, one would be choosing 1 card of 13 possible hearts, and 0 from the remaining 39 non-hearts. With respect to the entire deck, one would be choosing 1 card from 52 total cards. So the probability of drawing a heart is

$\dfrac{\dbinom{13}1\cdot\dbinom{39}0}{\dbinom{52}1}=\dfrac{13\cdot1}{52}=\dfrac14$

When Michelle replaces the card, the deck returns the normal, so the probability of drawing any card from a given suit is the same, $\dfrac14$ . In other words, drawing a spade is independent of having drawn the heart first.

So the probability of drawing a heart, replacing it, then drawing a spade is $\dfrac14\cdot\dfrac14=\dfrac1{16}$ .

4 0

2 years ago

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Suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marbl

ira [324]

4/9*3/9= 12/81=4/27
You have a 4 in 27 chance of drawing a red then a blue.

8 0

2 years ago

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Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Prope

ziro4ka [17]

Given:

Expression is

$3r^2-2r+4$

To prove:

If r is any rational number, then $3r^2-2r+4$ is rational.

Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.

Let r be any rational number.

We have,

$3r^2-2r+4$

It can be written as

$3(r\times r)-2r+4$

Now,

3, -2 and 4 are rational numbers by property 1.

$r^2=r\times r$ is rational by Property 3.

$3r^2\text{ and }-2r$ are rational by Property 3.

$3r^2+(-2r)+4$ is rational by property 2.

So, $3r^2-2r+4$ is rational.

Hence proved.

6 0

2 years ago

The number of bacteria, B, in a refrigerated food is given by the function b(t) = 15t2 - 60t + 125, where t is the temperature o

Nimfa-mama [501]

Answer: $b(t(h))=135h^2+180h+125$

Step-by-step explanation:

Given: The number of bacteria, B, in a refrigerated food is given by the function $b(t)=15t^2-60t+125$ , where t is the temperature of food in degrees Fahrenheit.