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There are 210 students in a twelfth grade high school class. 90 of these students have at least one sister and 105 have at least one brother. Out of these, there are 45 who have at least one sister and one brother.

Let A be the event that a randomly selected student in the class has a sister and B be the event that the student has a brother. Based on this information, answer the following questions.

What is P(A), the probability that the student has a sister? _____

What is P(B), the probability that the student has a brother?_____ 

What is P(A and B), the probability that the student has a sister and a brother? _____

What is P(B | A), the conditional probability that the student has a brother given that he or she has a sister? ____

Is P(B | A)=P(B)? Are the events A and B independent?

Guest Nov 23, 2018
 #1
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I can answer top 3. P(sister) would be 9/21

P(brother) would be 1/2

P(both) would be 195/210

tanmai79  Nov 23, 2018
 #2
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Sorry if i'm thinking too basically here. By the way, I'm 11 and don't understand the next parts to this question.

tanmai79  Nov 23, 2018
 #3
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P(both) is not 195/210

Guest Nov 23, 2018
 #4
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Oh, I get it. it's 15/21 or 5/7. I didn't count in the fact 45 students have both.

tanmai79  Nov 24, 2018
edited by tanmai79  Nov 24, 2018
 #6
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No, this is not the answer either.

Guest Nov 24, 2018
 #5
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P(B | A), the conditional probability that the student... Out of 210 students, 90 have at least one sister. There are 45 who have at least one sister and one brother. \(\dfrac{45}{90}\) simplifies to \(\dfrac{1}{2}\)

 

- PM

PartialMathematician  Nov 24, 2018
 #7
avatar+94183 
+1

There are 210 students in a twelfth grade high school class. 90 of these students have at least one sister and 105 have at least one brother. Out of these, there are 45 who have at least one sister and one brother.

Let A be the event that a randomly selected student in the class has a sister and B be the event that the student has a brother. Based on this information, answer the following questions.

 

What is P(A), the probability that the student has a sister? _____    \(\frac{90}{210}=\frac{3}{7}\)

 

What is P(B), the probability that the student has a brother?_____   \(\frac{105}{210}=\frac{1}{2}\)

 

What is P(A and B), the probability that the student has a sister and a brother? _____  \(\frac{45}{210}=\frac{3}{14}\)

 

What is P(B | A), the conditional probability that the student has a brother given that he or she has a sister?   \(\frac{45}{90}=\frac{1}{2}\)

 

Is P(B | A)=P(B)?   YES   Are the events A and B independent?   Yes I think they are independent.

 

Here is the corresponding Venn diagram.

 

Melody  Nov 24, 2018

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