A survey was conducted at a local dance studio asking students if they had ever competed in the following: Smooth Rhythm Standard .

Question

All three were 15

12 were NONE

smooth was 14

rhythm was 10

standard was 9

smooth and standard was 4

smooth and rhythm was 8

rythmn and standard was 13

If a student is chosen at random, what is the probability that the student competed in Rhythm GIVEN they had competed in Smooth. P(Rhythm∣Smooth) =

If a student is chosen at random, what is the probability that the student competed in Rhythm GIVEN they had competed in Standard.P(Rhythm∣Standard) =

If a student is chosen at random, what is the probability that the student competed in Standard GIVEN they had competed in Rhythm.P(Standard∣Rhythm) =

If a student is chosen at random, what is the probability that the student competed in Rhythm GIVEN they had competed in Smooth or Standard.P(Rhythm∣Smooth or Standard) =

Answer 1

Hi Holly T.,

So just draw the Venn diagram for the system. I note that the specific contents of each of the regions are supplied to you -- that's 8 regions in all. Usually, only data for aggregated regions are supplied, and you have to proceed through to determine each region population -- but not here, it's been handed you on a silver platter! Then, you must just add the various regions to obtain your corresponding populations to compare for probability. As an example, P(Rhythm|Smooth or Standard), smooth or standard population consists of areas of 14+8+15+4+13+9=63; Rhythm within those areas consists of 8+15+13=36; P=36/63.

Really, it's quick once you draw the Venn.

--Cheers, --Mr. d.