Ask question

Ask question

All categories

Romashka-Z-Leto [24]

3 years ago

13

There are 36 gold cards and 36 silver cards in a deck. The gold cards are numbered 1,3,5,... 71 and the silver cards are numbere

d 2.4.6,... 72. The cards are throughly shuffled and one card is randomly selected.
A. Find the probability of selecting a gold card or a card with a multiple of 12 on it. Show your work

B. Find the probability of selecting a silver card or a card with a multiple of 9 on it. Show your work.

2 answers:

Andrei [34K]3 years ago

8 0

A) multiples of 12 up to 72 ( 72 total cards)

12, 24, 36, 48, 60, 72 = 6 cards.

36 are gold.

Total gold cards and multiple of 12 = 36 + 6 =42

Probability of getting one of them is 42/72, which reduces to 7/12

B) 36 silver cards

Multiples of 9: 9, 18, 27, 36, 45, 54,63 = 7 cards

Silver cards are even and there is 3 even cards that are also multiples of 9, so subtract 3 from 7 to get 4.

Total silver cards and multiples of 9 = 36 + 4 = 40

Probability = 40/72 which reduces to 5/9

Yuki888 [10]3 years ago

6 0

Answer:

Step-by-step explanation:

A.

Because there is no overlap between good card and card with a multiple of 12,

P(gold card or a card with a multiple of 12)

= P(gold card) + P(a card with a multiple of 12)

P(gold card)

= no. of gold cards / total no. of cards

= 36 / (36 + 36)

= 36 / 72

= 1/2

P(a card with a multiple of 12)

= no. of cards with multiples of 12 / total no. of cards

= (12, 24, 36, 48, 60, 72) / 72

= 6/72

= 1/12

P(gold card or a card with a multiple of 12)

= 1/2 + 1/12

= 7/12

B. There ARE overlaps between a silver card and a card with a multiple of 9,

P(silver card or a card with a multiple of 9)

= P(silver card) + P(a card with a multiple of 9) - P(silver card AND a multiple of 9)

P(silver card)

= no. of silver cards / total no. of cards

= 36 / (36 + 36)

= 36 / 72

= 1/2

P(a card with a multiple of 9)

= no. of cards with multiples of 9 / total no. of cards

= (9, 18, 27, 36, 45, 54, 63, 72) / 72

= 8/72

= 1/9

P(silver card AND a multiple of 9)

= no. of silver cards AND a multiple of 9 / total no. of cards

= (18, 36, 54, 72) / 72

= 4/72

= 1/18

P(silver card or a card with a multiple of 9)

= 1/2 + 1/9 - 1/18

= 10/18

= 5/9

You might be interested in

Help please!!<br> 1. What is the value of n?<br> 2.What is the value of n?

lana66690 [7]

Using the intersecting chord theorem:

15 x 2 = 5 x n

Simplify:

30 = 5n

Divide both sides by 5:

n = 30/5

n = 6 m

8 x n+8 = 16 x n+2

Simplify:

8n +64 = 16n +32

Subtract 8n from both sides:

64 = 8n +32

Subtract 32 from both sides:

32 = 8n

Divide both sides by 8:

n = 32 /8

n = 4

4 0

4 years ago

Read 2 more answers

What is 12 divided by 8 as a fraction ( please explain)

marysya [2.9K]

1 1/2 or 3/2 because there is 4 more than 8 which is a half.

6 0

4 years ago

Read 2 more answers

The U.S Census Brureau has a population clock on the internet.On a recent day the United States population was listed as 310,763

goldfiish [28.3K]

Three hundred ten million, seven hundred sixty three thousand, one hundred thirty six

6 0

3 years ago

The point (2, –4) is reflected across the line y = –1. What are the coordinates of the image?

schepotkina [342]

ANSWER

The coordinates of the image are (2,2)

EXPLANATION

The mapping for a reflection across the line y=k is :

$(x,y)\to (x,2k-y)$

We want to find the image of the point (2,-4) after a reflection in the line y=-1.

In this case k=-1.

$(2, - 4)\to (2,2( - 1)- - 4)$

This simplifies to,

$(2, - 4)\to (2, - 2 + 4)$

$(2, - 4)\to (2, 2)$

Hence the image is (2,2)

4 0

3 years ago

Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

7 0

1 year ago