Mathematics, 28.05.2021 02:00 Geo777

According to a study, 50 % of adult smokers started smoking before 21 years old. 5 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded. a) The probability that at least 2 of them started smoking before 21 years of age is b) The probability that at most 4 of them started smoking before 21 years of age is c) The probability that exactly 3 of them started smoking before 21 years of age is

Answers: 1

Show answers

Answers

Answer from: keke6361

a) The probability that at least 2 of them started smoking before 21 years of age is 0.1875 = 18.75%.

b) The probability that at most 4 of them started smoking before 21 years of age is 0.96875 = 96.875%.

c) The probability that exactly 3 of them started smoking before 21 years of age is 0.3125 = 31.25%.

Step-by-step explanation:

For each smoker, there are only two possible outcomes. Either they started smoking before 21 years old, or they did not. Smokers are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

50% of adult smokers started smoking before 21 years old.

This means that p = 0.5

5 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.

This means that n = 5 .

a) The probability that at least 2 of them started smoking before 21 years of age is

This is:

$P(X \geq 2) = 1 - P(X < 2)$

In which

P(X < 2) = P(X = 0) + P(X = 1)

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125$

$P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625$

P(X < 2) = P(X = 0) + P(X = 1) = 0.03125 + 0.15625 = 0.1875

The probability that at least 2 of them started smoking before 21 years of age is 0.1875 = 18.75%.

b) The probability that at most 4 of them started smoking before 21 years of age is

This is:

$P(X \leq 4) = 1 - P(X = 5)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125$

$P(X \leq 4) = 1 - P(X = 5) = 1 - 0.03125 = 0.96875$

The probability that at most 4 of them started smoking before 21 years of age is 0.96875 = 96.875%.

c) The probability that exactly 3 of them started smoking before 21 years of age is

This is P(X = 3). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125$

The probability that exactly 3 of them started smoking before 21 years of age is 0.3125 = 31.25%.

Answer from: Quest

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

$\begin{bmatrix}1 & 0 & 0& |5 \\ 0& 2& 0& |8\\ 0& 0& 3& |9\end{bmatrix}$

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

$\begin{bmatrix}1 & 0 & 0& |5 \\ 0& 1& 0& |4\\0& 0& 1& |3\end{bmatrix}$

What is the next step in solving this augmented matrix using gauss-jordan elimination method

Answer from: Quest

The right answer should be 6 but your not very specific

Questions in other subjects:

History, 04.12.2020 20:30

Pls answer here are some points ...

History, 04.12.2020 20:30

neil thisse is a loyalist who fled the colonies during the revolution and has returned to reclaim his property in dover ma according to the treaty of paris be entitled to his land....

English, 04.12.2020 20:30

How can I get revenge on my cousin for getting me in trouble all the time for no reason I need ways to get revenge that will be hard for my aunt and uncle to know it was me!...

Social Studies, 04.12.2020 20:30

Free POINTS! who wants to be my friend?...

History, 04.12.2020 20:30

56 days is equivalent to how many seconds?...

Mathematics, 04.12.2020 20:30

Sour Patch Kids cost $ 3.00 per pound. For each question, explain or show your reasoning. How. any pounds of Sour Patch Kids can you buy for $1.00? ○ 1/2 or 0.5 lbs○ 3 lbs

Biology, 04.12.2020 20:30

Human blood type has 3 alleles that can be inherited: A, B, O. Individuals can also inherit type AB blood. What two terms best describe the inheritance patterns of blood...

Mathematics, 04.12.2020 20:30

Problem How many solutions does the system have? \begin{cases} y = -2x-4 y = 3x+3 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y...

Health, 04.12.2020 20:30

Why do teens choose to avoid tobacco 1.they think that smoking has no negative effects on younger people 2.they want to seem or feel more mature 3.they want to look li...

Mathematics, 04.12.2020 20:30

What are the solutions of the inequality? Graph the solutions given: -19 < 3x - 4 < 5...

More questions: Mathematics Another questions

Answers

Other questions on the subject: Mathematics

Questions in other subjects: