Question

In a high school orchestra there are 3 training groups: one is Violin, one in Flute, and one in Cello. These sections are open to any of the 100 students in the school. There are 36 students in the Violin group, 30 in the Flute group, and 27 in the Cello group. There are 9 students that are in both Violin and Flute, 18 that are in both Violin and Cello, and 6 are in both Flute and Cello. In addition, there are 4 students taking all 3 sections. If a student chosen at random,

a) the probability that he is not included in any of these groups is?

b) the probability that he is playing exactly one instrument group is?

c) When two people are chosen randomly, the probability that at least 1 is in an instrument group is?

Answer 1

let

V represent Violin

F represent flute

C represent Cello

we have given that P(F) =36/100 =0.36 P(F)=30/100=0.30 P(C) =27/100 =0.27

a)

we have to find probability of a student who have not joined the instrument class so

first find the probability of student who have joined at least one instrument which is given by

so required Probability is

b)

we have to find the probability that he is playing exactly one instrument group is

which is given by

now

now

c)

P( in instrument group ) =p=0.64 (from a part)

we have two students

P( at least on from instrument group) =1-P(both are from non-instrument group)

=1-0.36*0.36

=1-0.1296

=0.8704