chasebraves
  • chasebraves
FOR A MEDAL
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
chasebraves
  • chasebraves
A class of 160 students contains 40 honor students, 60 athletes, and 80 who are neither athletes nor honor students. From the entire group a student is chosen at random. What is the probability that the student chosen is an honor student given that he is an athlete?
anonymous
  • anonymous
is it multiple choice?
anonymous
  • anonymous
2:4

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More answers

jchick
  • jchick
Ah good old probablility
anonymous
  • anonymous
i think
chasebraves
  • chasebraves
here r the answers 1/8 1/3 1/2
jchick
  • jchick
Once you know he is an honor student, the denominator drops from 160 to just 40. And since 40 + 60 + 80 is 180 but there are only 160 students, 20 were counted twice so they must be both honor and athletes. So it's 20/40 or 1/2 that the student chosen is an athlete given that he is an honor student
chasebraves
  • chasebraves
can u help me with some more questions
jchick
  • jchick
Yup
chasebraves
  • chasebraves
A class of 160 students contains 40 honor students, 60 athletes, and 80 who are neither athletes nor honor students. From the entire group a student is chosen at random. What is the probability that the student chosen is an athlete given that he is an honor student? 1/8 1/4 1/2
jchick
  • jchick
Same question?
chasebraves
  • chasebraves
nope
jchick
  • jchick
Oh slight difference
chasebraves
  • chasebraves
yep
jchick
  • jchick
|dw:1450111334533:dw|
jchick
  • jchick
|dw:1450111476941:dw|
jchick
  • jchick
Total students can be called s = 160
jchick
  • jchick
On the first one the total must be 160 inside. right now we have 80 + 40 + 60 = 180 which is 20 too many. that's how many honor students are also athletes.
jchick
  • jchick
So 1/9.
jchick
  • jchick
the other way you could do this is using probability statements.
jchick
  • jchick
Have you talked about unions and intersections?
jchick
  • jchick
∪ means union which means "OR"
jchick
  • jchick
∩ means intersection which means "AND" does that seem familiar?
jchick
  • jchick
@chasebraves
jchick
  • jchick
@mathmale should I explain this way?
chasebraves
  • chasebraves
ok
jchick
  • jchick
Ok so does that sound familiar?
chasebraves
  • chasebraves
yes can u help me with one more
chasebraves
  • chasebraves
A box contains 6 red and 5 blue marbles. Another box contains 5 red and 8 blue marbles. One box is selected at random and from that bag, one marble is drawn. What is the probability that the marble drawn is blue?
jchick
  • jchick
Wait I didn't finish with that method I didn't know if you knew that yet
chasebraves
  • chasebraves
oh ok
jchick
  • jchick
The rule is: P(A∪B)=P(A)+P(B)−P(A∩B) now we have the other one. ∩ means intersection which means "AND", that is P(A∩B) means the probability of A and B both occuring. you shold have also come across A′=AC which means the complement of A which means everything not in A. So this means that A together with AC will include all possibilities.
jchick
  • jchick
okay, so with the complement, this means that P(A)+P(AC)=1 because everything that isn't in A is in A'. So if we let A=(H∪J) where H is if the student is an Honor student and J is if the student is an athlete ( or Jock). then this becomes P(A)+P(AC)=P(H∪J)+P((H∪J)C)=1 but P(H∪J)=P(H)+P(J)−P(H∩J) and P((H∪J)C)=P(HC∩JC) so all of this becomes P(H)+P(J)−P(H∩J)+P(HC∩JC)=1⇒P(H∩J) =P(H)+P(J)+P(HC∩JC)−1=40160+60160+80160−160160=20160
jchick
  • jchick
Those didn't come out
chasebraves
  • chasebraves
ok
jchick
  • jchick
1 = 40/160 + 60/160 + 80/160 - 160/160 = 20/160
jchick
  • jchick
P(A∪B)=P(A)+P(B)−P(A∩B) is the rule this is the Probability of A plus the Probability of B minus the probability of their intersection. I forgot to mention that if A and B are mutually exclusive, meaning they cannot happen at the same time or that you can't have both occurring, then P(A∩B)=0(only if A and B are MUTUALLY EXCLUSIVE). P(A∩B) is the Probability of A and B occurring at the same time (simultaneously). P(AC)=1−P(A) is the Probability of everything NOT in A. Additionally, (A∪B)C=(AC∩BC)
jchick
  • jchick
So that is that.
chasebraves
  • chasebraves
ok
jchick
  • jchick
20/160 can be reduced to 1/8
jchick
  • jchick
I forgot that.
jchick
  • jchick
So to start with you have 11 Red or R and you have 13 Blue or B
jchick
  • jchick
So your probability is found by adding then dividing
jchick
  • jchick
Together we have 24 marbles.
jchick
  • jchick
Now we take and divide our B by the RB
jchick
  • jchick
Or you take 24 and divide by 13
jchick
  • jchick
@mathmale I am having trouble with the next part
jchick
  • jchick
|dw:1450114604460:dw|
jchick
  • jchick
|dw:1450115296671:dw|
jchick
  • jchick
|dw:1450115405702:dw|
jchick
  • jchick
|dw:1450115564680:dw|
jchick
  • jchick
53.5 % is your final answer

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