In a particular college, an exchange programme qualification test involves two stages: a written tes

Question

In a particular college, an exchange programme qualification test involves two stages: a written test and an interview. To qualify for the exchange programme, a student must first pass the written test and then the interview. Students who fail the written test at the first attempt will be required to take a second attempt. Students are given only one attempt at the interview. The probability that a student passes the written test, on either attempt, is $0.7$. The probability that a student passes the interview is $0.4$. Draw a tree diagram to represent this information.[3] Show that the probability of a student qualifying for the exchange programme is $0.364$.[2] Find the probability that a student fails the written test in the first attempt, given that the student qualifies for the exchange programme.[3] $20$ students take the exchange programme qualification test. The results of all the students are independent of each other. Find the probability that at least $14$ of the students qualify for the exchange programme.[3]

Accepted Answer

(c)0.231 (d)0.00235

2024 NYJC H1 Q10

2024 NYJC H1 Q10