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andrew11 [14]
3 years ago
13

There are 200 students in an eleventh-grade high school class. There are 40 students in the soccer team and 50 students in the b

asketball team. Out of these students, there are 10 who play on both teams.
Let A be the event that a randomly selected student plays soccer and B be the event that the student plays basketball. Based on this information, answer the following questions.
What is P(A) the probability that the student plays soccer?
What is P(B) the probability that the student plays basketball?
What is P(A and B) the probability that the student plays soccer and basketball?
What is P(A | B) the conditional probability that the student plays soccer given that he or she plays basketball?

Is P(A | B)=P(A)? Are events A and B independent?
Choose all answers that apply:

(Choice A)
Yes, P(A | B)=P(A)

(Choice B)
No, P(A | B)≠P(A)

(Choice C)
Yes, events A and B independent events.

(Choice D)
No, events A and B are not independent events.
Mathematics
1 answer:
Dvinal [7]3 years ago
3 0

Answer:

1/5,1/4,1/20, yes, yes

Step-by-step explanation:

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Answer:

a) In the year 1998 with 3 days, 2 hours, 44 minutes and 18.1006141 seconds

b) In the year 1998 with 19 days, 18 hours, 5 minutes and 35.10875472 seconds

Step-by-step explanation:

a) To know the time when the population will be 305 million people, we need to isolate the variable t in the equation, P(t)=288(1.009)^{t-1997}

So we isolate t with the property of logarithms that allow us go down the exponent, applying in both sides of the equation

For this subsection the value of P is equal to 305 million people

Ln(305)=Ln[(288)(1.009)]^{t-1997}

Ln(305)=(t-1997)*Ln[(288)(1.009)]

Now, we can isolate the value of t

\frac{Ln(305)}{Ln[(288)(1.009)]} =t-1997

\frac{Ln(305)}{Ln[(288)(1.009)]}-1997 =t

t=1998.008531776402

So to know the exact date we multiply the number after the point, that is 0.008531776402 for the number of days that have 1 year, equal to 365 days

0.008531776402*365= 3.114098387 days

then the number after the point, that is 0.114098387 will be multiply for the number of hours that have 1 day

0.114098387*24= 2.738361282 hours

then the number after the point, that is 0.738361282 will be multiply for the number of minutes that have 1 hour

0.738361282*60= 44.3016769 minutes

Finally, the number after the point, that is 0.3016769 will be multiply for the number of seconds that have 1 minute

0.3016769*60= 18.1006141 seconds

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b) For calculate the time when the population is 395 million people, we do the same process we did in the subsection a)

Ln(395)=Ln[(288)(1.009)]^{t-1997}

Ln(395)=(t-1997)*Ln[(288)(1.009)]

Now, we can isolate the value of t

\frac{Ln(395)}{Ln[(288)(1.009)]} =t-1997

\frac{Ln(395)}{Ln[(288)(1.009)]}-1997 =t

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0.05412021527*365= 19.75387857 days

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0.09308577*60= 5.585145912 minutes

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And we obtain that the time, when the population of the country is 395 million people, is in the year 1998 with 19 days, 18 hours, 5 minutes and 35.10875472 seconds

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