A school employs math teachers and physics teachers. If 4 of these

Question

A school employs math teachers and physics teachers. If 4 of these teachers are selected randomly, what is the probability that at least one math teacher is selected?

(1) The ratio of the number of physics teachers to the number of math teachers is 2 to 1.
(2) The sum of the number of physics teachers and the number of math teachers is 24.

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ManifestDreamMBA · Answer

P(At least one math) = ?

Statement 1
P(Physics) = 2/3
P(Math) = 1/3
P(At least one math) = 1 - P(none math)
= 1 - (2/3)^4
Sufficient

Statement 2
P+M = 24
We don't know the split b/w P and M to know the probability of picking them individually
Insufficient

Answer A

ravi1522 · Answer

Hello ,
Probability for At least one math Teacher can be 1-(probability of no Maths teacher )
As per statement 1
the ratio of both teacher given so we can get the probability as 
1-(2k/(k+2k)^4
Hence sufficient

As per statement 2 total no of teacher is given 
so we cannot find probability as we need count of individual teacher as well

Hence option A is correct

HarshavardhanR · Answer

How do we calculate what is asked?

P (at least 1 math teacher selected) = 1 - P (not even one math teacher selected) = 1 - P (all 4 teachers selected are physics teachers)

Statement 1

P:M = 2:1. So, let P = 2x and M = x. Total number of teachers = 3x.

P (all 4 teachers selected are physics teachers) =  \frac{2x}{3x}  *  \frac{(2x-1)}{(3x-1)}  *  \frac{(2x-2)}{(3x-2)}  *  \frac{(2x-3)}{(3x-3)}

Sidenote:  We can also arrive at the above using  \frac{2xC4 }{ 3xC4}

Observe : we  do not have enough information  to find the above Probability. If we knew x, for instance, we would be able to calculate the exact value of the above. Not the case!

Thus,

P (all 4 selected are physics teachers) -> information not sufficient to calculate this.
So,
P (at least 1 math teacher selected) = 1 - above Probability -> information not sufficient to calculate this.

Statement 1 alone is not sufficient.

Statement 2

Clearly, this statement is also not sufficient. The probability will change based on the exact split of physics and math teachers.

Statements 1 and 2 together

2x + x = 3x = 24 => x = 8.

So,
P -> 16
M -> 8

P (all 4 selected are physics teachers) -> calculable ( \frac{16}{24}  *  \frac{15}{23}  *  \frac{14}{22}  *  \frac{13}{21} )

P (at least 1 math teacher selected) -> calculable (1 -  \frac{16}{24}  *  \frac{15}{23}  *  \frac{14}{22}  *  \frac{13}{21} )

Statements 1 and 2 are together sufficient. Choice C.

---
Harsha

Abhiswarup · Answer

Answer should be C.

No. of Mathematics teacher= x
No. of Physics teacher=2x
 Thus one can't tell how many teachers are for mathematics and how many for physics.
Statement one is not sufficient.

Total teachers is 24, Statement is not sufficient to tell how many are mathematics and how many are physics. Combined we get
Physics Teacher = 16
Mathematics Teacher= 8

Probability of selecting at least one mathematics teacher= (16C3*8C1+16C2*8C2+16C1*8C3+8C4)/24C4

Thus both statements are needed for answering the question.

Correct answer is C

A school employs math teachers and physics teachers. If 4 of these

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GMAT Data Sufficiency (DS) Questions

A school employs math teachers and physics teachers. If 4 of these

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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