Turn on thread page Beta
    • Thread Starter

    Printer Cartridges are defective with probability p, independently of each other.

    a) Cartridges are inspected one at a time. What is the probability that the 5th cartridge inspected is the 2nd defective? what is the expected number of inspections required to find 2 defectives?

    My answers were 4p2q3 and 2/p are these right?

    b) How many cartridges should you buy, to ensure a probability of at least 0.99 that at least one of them works?

    There are 60 students in a class. 40 of them know that a random variable is a rule for allocating numbers to the outcomes of an experiment. These are 'good' students. A tutorial group contains 10 students, samples independently from the class.

    a) what is the probability that the group contains exactly 8 good students?

    b) What is the probability that the group contains more food students than average?

    c) In fact the group contains 5 good students. Their tutor asks to see all 10 students in turn. What is the probability that the sixth student seen is the 3rd good one?

    Are my answers right? and can someone help me with 1b. thanks


    We want the smallest n such that

    P(n cartridges are all faulty) <= 0.01
    p^n <= 0.01
    n log(p) <= log(0.01)
    n >= log(0.01)/log(p) . . . . . log(p) is negative!

    So the smallest possible n is log(0.01)/log(p) rounded up to the nearest integer.

    You can't use a binomial random variable because the sample is taken without replacement.

    40C8*20C2 / 60C10 = 0.194

    Average = 6.67 good students.

    P(more than average good students)
    = P(7 good students) + P(8 good students) + P(9 good students) + P(10 good students)
    = (40C7*20C3 + 40C8*20C2 + 40C9*20C1 + 40C10) / 60C10
    = 0.559

    There are 10C5 strings that consist of five "0"s and five "1"s.

    The number of these strings that have a "1" in position 6 and exactly two "1"s in positions 1-5 is

    5C2 [choose two positions from 1-5 to be "1"s]
    *4C2 [choose two positions from 7-10 to be "1"s]

    = 5C2*4C2/10C5
    = 5/21
    • Thread Starter


University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Black Friday: Yay or Nay?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way


Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.