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lozanna [386]
3 years ago
9

Suppose that in a certain population of married couples, 30% of the husbands smoke, 20% of the wives smoke, and in 8% of the cou

ples both the husband and the wife smoke. Is the smoking status (smoker or non-smoker) of the husband independent of that of the wife? Why or why not?
Mathematics
1 answer:
xxTIMURxx [149]3 years ago
6 0

Answer:

Not independent

Step-by-step explanation:

Given that in a certain population of married couples, 30% of the husbands smoke, 20% of the wives smoke, and in 8% of the couples both the husband and the wife smoke.

Let A be the event that husbands smoke and B the event that wives smoke

Give that

P(A) = 0.30\\P(B) = 0.20\\P(A\bigcap B) = 0.08

To check whether A and B are independent it is sufficient to check

P(A\bigcap B)=P(A)P(B)

Right side=P(A)P(B)\\=0.3(0.2)\\=0.06

Left side = 0.08

Since two sides do not equal the two events are not independent.

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Julian walked 6/10 of a mile to his friends house and another 35/100 mile to the store. He walked 1/4 of a mile back home. Julia
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The statement, "Julian's sister said he walked 1/5 mile" cannot be agreed because Julian totally walked 1\frac{1}{5} \text{ or } \frac{6}{5} miles.

<u>Solution:</u>  

Given that,

  • Julian walked 6/10 of a mile to his friends house
  • Another 35/100 mile to the store
  • He walked 1/4 of a mile back home

To find total distance walked by Julian we have to add the above stated values. That is, \frac{6}{10} +\frac{35}{100} +\frac{1}{4}

Factors of 10 = 5\times2

Factors of 100 = 5\times2\times5\times2

Factors of 4 = 2\times2

Therefore, the least common factor of 10, 100 and 4 is 100. With like denominators we can operate on just the numerators,

\frac{6\times10}{10\times10} +\frac{35\times1}{100\times1} +\frac{1\times25}{4\times1}\rightarrow\frac{60+35+25}{100}\rightarrow\frac{120}{100}

\Rightarrow\frac{120}{100}\rightarrow\frac{6}{5}

Which can also be written as 1\frac{1}{5}.

So, from the above calculation it can be said that Julian walked 1\frac{1}{5} \text{ miles }.

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Step-by-step explanation:

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given \frac{(x-3)(x-2)}{(x+3)(x-3)}

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