Question

in an examination, 30% of the students have failed in engineering mechanics, 20% of the students have failed in mathematics nd 10% have failed in both the subjects. a student is selected at random. 1). what is the probability that the student has failed in engineering mechanis if it is known that he has failed in mthematics? , 2). wht is the probability that the student has failed either in engineering mechanics or in mathematics?

Answer 1

We know that P(A)=0.3; P(B)=0.2; P(A∩B)=0.1. Thus,
1). P(A│B)=(P(A∩B))⁄(P(B))=0.1⁄0.2=0.5.
2). P(A∪B)=P(A)+P(B)-P(A∩B)=0.3+0.2-0.1=0.4.

Answer:
1). The probability the student has failed in engineering mechanics if it is known that he has failed in mathematics is 0.5.
2). The probability that the student has failed either in engineering mechanics or in mathematics is 0.4.