Question

2. One white ball, one black ball, and two yellow balls are placed in a bucket. Two balls are drawn simultaneously from the bucket. You are given the information that at least one of them is yellow. What is the probability that the second ball is also yellow?

3. Students taking the GMAT were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows. a. If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate engineering major? b. If a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree?

4. Two fair dice are rolled and the upper sides (faces) are recorded. Given information that the sum of the faces equals to 10, what is the probability that the first one has a 5 on the face?

Answer 1

2)

P(at least one ball is yellow)=1-P(none is yellow) =1-(2/4)*(1/3)=5/6

P(both are yellow) =(2/4)*(1/3) =1/6

therefore P(2nd is yellow|at least one yellow) =P(both yellow)/P(At least one is yellow)

=(1/6)/(5/6)=1/5

3)

summary of the data is not shown in the problem, please provide data table for this

4)

P(sum is 10) =3/36   (there are 3 such outcomes (4,6),(5,5),(6,4))

P(sun 10 and 1st dice show 5) =1/36 (only one such outcome of (5,5))

therefore P( first one has a 5 |sum of 10) =P(sun 10 and 1st dice show 5)/P(sum is 10)

=(1/36)/(3/36)

=1/3