A guidance counselor reports that in a given semester, the probability that a student chooses art as an elective is 15 percent, the probability that a student chooses art or drama is 20 percent, and the probability that a student chooses both art and drama is 2 percent. What is the probability that a student chooses drama as an elective?
Answers
The probability that a student chooses drama as an elective is 0.07 or 7%.
Explanation:
Let A = Event that student chooses art .
D= Event that student chooses drama .
As per given , we have
P(A) =0.15
P(A or B)= 0.20
P(A and B)=0.02
To find : P(B)
Using formula : P(A or B)= P(A)+P(B)-P(A and B)
Substitute all the value in the above formula , we get
0.20= 0.15+P(B)-0.02
⇒ P(B)= 0.20- 0.15+0.02=0.07
Therefore , the probability that a student chooses drama as an elective is 0.07 or 7%.
# Learn more :
In a class, all students take part in either music or drama or both. 25 students take part
in music, 30 students take part in drama and 8 students take part in both music and
drama. Find
(i) The number of students who take part in only music.
(ii) The number of students who take part in only drama.
(iii) The total number of students in the class.
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