SOLUTION: Out of forty students, there are 14 who are taking Physics and 29 who are taking Calculus. What is the probability that a randomly chosen student from this group is taking only the

Algebra ->  Probability-and-statistics -> SOLUTION: Out of forty students, there are 14 who are taking Physics and 29 who are taking Calculus. What is the probability that a randomly chosen student from this group is taking only the      Log On


   



Question 860119: Out of forty students, there are 14 who are taking Physics and 29 who are taking Calculus. What is the probability that a randomly chosen student from this group is taking only the Calculus class?
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi,
Phy 14
Cal 29
43 (3 both) That is: 11 + 26 + 3 = 40
only Calculus 26
P(only calculus) = 26/40 = 1320

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor is correct. However let's use the formulas:

P(A OR B) = P(A) + P(B) - P(A AND B)

P(X) = P(X and Y) + P(X and Y')

and a little more detail, in case you need it.

We will assume that all 40 are taking either physics or calculus or both,
and that there are no students of the 40 who are not taking at least one
of them.  (Otherwise there would be more than one solution).
So the probability that they are taking one or the other or both
is assumed to be 1.

There are four categories the 40 students can be in

#1. Those taking physics but not calculus.
#2. Those taking BOTH physics and calculus.
#3. Those taking calculus but not physics.  <-- what we are looking for!
#4. Those NOT taking either physics or calculus.

     P(calculus) = P(#2) + P(#3)

A)         29/40 = P(#2) + P(#3)

P(physics OR calculus) = P(physics) + P(calculus) - P(physics AND calculus)

               1 = 14/40 + 29/40 - P(#2)

Multiply through by 40

              40 = 14 + 29 - 40P(#2)
              40 = 43 - 40P(#2)
         40P(#2) = 3
           P(#2) = 3/40

Substitute in equation A)

A)         29/40 = P(#2) + P(#3)
           29/40 =  3/40 + P(#3)
           26/40 = P(#3)
           13/20 = P(#3) 

Edwin