Ask question

Ask question

All categories

vagabundo [1.1K]

3 years ago

6

Suppose that 45% of people have dogs. If two people are randomly chosen, what is the probability that they both have a dog

1 answer:

mylen [45]3 years ago

4 0

Answer:

$P(Dogs) = 0.2025$

Step-by-step explanation:

Given

$Proportion, p = 45\%$

Required

Probability of two people having dog

First, we have to convert the given parameter to decimal

$p = \frac{45}{100}$

$p = 0.45$

Let P(Dogs) represent the required probability;

This is calculated as thus;

<em>P(Dogs) = Probability of first person having a dog * Probability of second person having a dog</em>

<em />

$P(Dogs) = p * p$

$P(Dogs) = 0.45 * 0.45$

$P(Dogs) = 0.45^2$

$P(Dogs) = 0.2025$

<em>Hence, the probability of 2 people having a dog is </em> $P(Dogs) = 0.2025$ <em />

You might be interested in

Probabilities with possible states of nature: s1, s2, and s3. Suppose that you are given a decision situation with three possibl

amm1812

Answer:

1. $P(s_1|I)=\frac{1}{11}$

2. $P(s_2|I)=\frac{8}{11}$

3. $P(s_3|I)=\frac{2}{11}$

Step-by-step explanation:

Given information:

$P(s_1)=0.1, P(s_2)=0.6, P(s_3)=0.3$

$P(I|s_1)=0.15,P(I|s_2)=0.2,P(I|s_3)=0.1$

(1)

We need to find the value of P(s₁|I).

$P(s_1|I)=\frac{P(I|s_1)P(s_1)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_1|I)=\frac{(0.15)(0.1)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_1|I)=\frac{0.015}{0.015+0.12+0.03}$

$P(s_1|I)=\frac{0.015}{0.165}$

$P(s_1|I)=\frac{1}{11}$

Therefore the value of P(s₁|I) is $\frac{1}{11}$ .

(2)

We need to find the value of P(s₂|I).

$P(s_2|I)=\frac{P(I|s_2)P(s_2)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_2|I)=\frac{(0.2)(0.6)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_2|I)=\frac{0.12}{0.015+0.12+0.03}$

$P(s_2|I)=\frac{0.12}{0.165}$

$P(s_2|I)=\frac{8}{11}$

Therefore the value of P(s₂|I) is $\frac{8}{11}$ .

(3)

We need to find the value of P(s₃|I).

$P(s_3|I)=\frac{P(I|s_3)P(s_3)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_3|I)=\frac{(0.1)(0.3)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_3|I)=\frac{0.03}{0.015+0.12+0.03}$

$P(s_3|I)=\frac{0.03}{0.165}$

$P(s_3|I)=\frac{2}{11}$

Therefore the value of P(s₃|I) is $\frac{2}{11}$ .

4 0

3 years ago

Devon will drive 7×3 or 21 miles in 7 hours. Logan will drive 7×3 or 21miles in 7 hours so logan will drive _ or how many miles

natulia [17]

Answer: I believe you answered your own question 21.

Step-by-step explanation: Logan will drive 7×3 or 21miles in 7 hours

8 0

3 years ago

What’s the answer for this hurry

Flura [38]

Answer:

Step-by-step explanation:

Converse

7 0

3 years ago

Use the drop-down menus to describe the key aspects of the function f(x) = –x2 – 2x – 1.

Margaret [11]

Answer: The vertex is the minimum value

The function is increasing when x<1

The function is decreasing when x>1

The domain of the function is all real numbers

The range of the function is all numbers less than it equal to 0

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Angelica reads 15 pages of a book each day. In 10 days, she reads 200 pages. Assume the relationship is linear. Find and interpr

Phantasy [73]

Given:

Angelica reads 15 pages of a book each day.

In 10 days, she reads 200 pages.

Assume the relationship is linear.

To find:

The rate of change and initial value.

Solution:

The slope intercept form of a linear function is:

$y=mx+b$ ...(i)

Where m is the slope and b is the y-intercept.

Angelica reads 15 pages of a book each day. So, the rate of change is 15 pages per day and $m=15$ .

In 10 days, she reads 200 pages. It means the linear relation passes through the point (10,200).

Putting $x=10,y=200,m=15$ in (i), we get

$200=15(10)+b$

$200=150+b$

$200-150=b$

$50=b$

So, the y-intercept is 50. It means the initial number of pages angelica already read is 50.

Therefore, the rate of change is 15, it means Angelica reads 15 pages per day. The y-intercept is 50, it means the initial number of pages angelica already read is 50.

5 0

3 years ago