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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

Mathematics
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 />

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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}.

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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
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Step-by-step explanation:

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Given:

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

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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
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