Question

Joshua is doing Matric and has applied to enrol at a university of technology next 

year. The requirements for him to secure a place at the university is that he 

should pass English and at least two other subjects from the three subjects: 

Mathematics, Physical Science and Technical Drawing. The principal at Joshua’s 

school has determined the probabilities of him passing English is 0.7 and him 

passing each of the three other subjects as 0.6, 0.9 and 0.8, respectively.

Assuming that the event of Joshua passing any of the four subjects is 

independent of him passing any of the other subjects, calculate the probability 

that Joshua will secure a place at the university

Answer 1

Let A - "Joshua will secure place", B - "Joshua passed English", H1 - "Joshua passed Mathematics", H2 - "Joshua passed Physical science", H3 - "Joshua passed Technical drawing", then, since the probabilities of passing test are independent from each other:

$P(A)=P(B)*(P(H1)*P(H2)*P(\neg H3)+P(H1)*P(H3)*P(\neg H2)+P(H2)*P(H3)*P(\neg H1)+P(H1)*P(H2)*P(H3))=0.7*(0.6*0.9*0.2+0.6*0.8*0.1+0.9*0.8*0.4+0.6*0.9*0.8)=0.7*0.876=0.6132$