The probability that the randomly selected student exactly likes exactly one of the three types is 0.72
<h3>What is a probability?</h3>
It is a branch of mathematics. It is used to concern numerical descriptions to occur an event. Theoretical probability, Experimental probability, Axiomatic probability are the three types of probability we have. Probability can be expressed in proportions. Probability deals in finding the occurrence of an event. The theoretical probability is based on possible chances of something that happen. Probability refers to the term synonymously as a possibility. The probability that is based on series of experiments is known as Experimental probability. The set of axioms which are applied to all the types of probability is known as Axiomatic probability.
Number of persons who likes rock music be R
Number of persons who likes Country music be C
Number of persons who likes Jazz music be J
R = 206
C = 158
J = 119
R ∩ C = 26 - 7 = 19
R ∩ J = 27 - 7 = 20
C ∩ J = 19 - 7 = 12
R ∩ C ∩ J = 7
Thus, number that liked only jazz music is;
n(only jazz) = J - [(R ∩ J) + (C ∩ J) + (R ∩ C ∩ J)]
n(only jazz) = 119 - (20 + 12+ 7)
n(only J) = 119-39=80
Number of students that liked only Rock music;
n(only Rock) = R - [(R ∩ C) + (R ∩ J) + (R ∩ C ∩ J)]
n(only Rock) = 206 - (19 + 20 + 7)
n(only R) = 206-46=160
Number of students that liked only country music;
n(only country) = C - [(R ∩ C) + (C ∩ J) + (R ∩ C ∩ J)]
n(only country) = 158- (19 + 12 + 7)
n(only C) = 158-38=120
The probability that the randomly selected student exactly likes exactly one of the three types is,
P= (80+160+120)/500
P=360/500
P=0.72
Therefore, the probability is 0.72.
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