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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?
is it multiple choice?
Ah good old probablility
here r the answers 1/8 1/3 1/2
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
can u help me with some more questions
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
Oh slight difference
Total students can be called s = 160
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.
the other way you could do this is using probability statements.
Have you talked about unions and intersections?
∪ means union which means "OR"
∩ means intersection which means "AND" does that seem familiar?
@mathmale should I explain this way?
Ok so does that sound familiar?
yes can u help me with one more
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?
Wait I didn't finish with that method I didn't know if you knew that yet
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.
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
Those didn't come out
1 = 40/160 + 60/160 + 80/160 - 160/160 = 20/160
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)
So that is that.
20/160 can be reduced to 1/8
I forgot that.
So to start with you have 11 Red or R and you have 13 Blue or B
So your probability is found by adding then dividing
Together we have 24 marbles.
Now we take and divide our B by the RB
Or you take 24 and divide by 13
@mathmale I am having trouble with the next part
53.5 % is your final answer