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# (Solved): EXERCISE 8 An English proficiency test has 30 multiple-choice questions. Each question has five opti ...

EXERCISE 8 An English proficiency test has 30 multiple-choice questions. Each question has five options and only one option is correct. (a) If a student made random guess for each question, find the probability that he get (i) no correct answer (3 marks) (ii) more than 10 correct answers (3 marks) (b) If 5 students guessed at each of the answers, determine the probability that only one student did not get any correct answer. (4 marks) EXERCISE 9 A manufacturer produces bottles of mineral water. The mineral water is sold in boxes containing 25 bottles of mineral water each. The probability that a bottle of mineral water from a box is defective is 0.1 . A box is selected at random. i. Find the probability that no bottle of mineral water is defective. (2 marks) ii. Find the probability that between three and seven bottles are defective. (2 marks) iii. A company purchases 10 boxes containing bottles of mineral water from the manufacturer. What is the probability that at least one of the boxes contains no defective bottles of mineral water? (3 marks) EXERCISE 10 A census on population in urban areas in Malaysia had been conducted. The census revealed that almost

`65%`

of all households in urban areas in Malaysia were composed of at most two persons per household. Assuming that this percentage is still valid today, what is the probability that: a) Out of 10 households selected, not more than 8 households composed at most 2 persons. (0.9140) b) More than 3 households of the next 10 households are composed of more than 2 persons.

`(0.4862)`

EXERCISE 11 MY Bank customers arrive randomly on weekday afternoons at an average of 4 customers every 5 minutes. What is the probability that: a) Exactly 5 customers will arrive in a 5 -minute interval on a weekday afternoon? (0.1563) b) Not more than 3 customers will arrive in a 10 -minute interval on a weekday afternoon? (0.04238)

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