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  1. #1
    Senior Member slevvio's Avatar
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    easy peasy

    Hello I was wondering if I could some help with this question. I am good at the hard stuff but it is the simple things like this which perplex me.

    A cheap mass-produced pencil sharpener is encased in a plastic imitation of a World Cup football. About 20% of all sharpeners have loose fitting blades. Similarly about 10% have blunt blades. Assume that the blades are produced independently of each other and are subsequently fitted to the plastic footballs by independent operations of an assembling machine.

    Determine the probabilities of the following events:

    (i) that a randomly selected sharpener has both defects;
    (ii) that a randomly selected sharpener has a loose fitting blade which is not blunt;
    (iii) that a randomly selected sharpener has a blunt blade which is not loose fitting;
    (iv) that a randomly selected sharpener has neither defect.

    I know it has something to do with independence but I'm just not sure what to do with it. Thanks a lot.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by slevvio View Post
    Hello I was wondering if I could some help with this question. I am good at the hard stuff but it is the simple things like this which perplex me.

    A cheap mass-produced pencil sharpener is encased in a plastic imitation of a World Cup football. About 20% of all sharpeners have loose fitting blades. Similarly about 10% have blunt blades. Assume that the blades are produced independently of each other and are subsequently fitted to the plastic footballs by independent operations of an assembling machine.

    Determine the probabilities of the following events:

    (i) that a randomly selected sharpener has both defects;
    0.2*0.2

    (imagine 1000 sharpeners 200 have the first defect and of these 40 have
    the second as well)

    (ii) that a randomly selected sharpener has a loose fitting blade which is not blunt;
    0.2*0.8

    and the rest follow the same basic idea

    RonL
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  3. #3
    Senior Member slevvio's Avatar
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    Thank you for responding but would the first answer not be 0.2 * 0.1 using that logic? That is 20% of the sharpeners have the defect, and 10% of that 20% have the other defect?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by slevvio View Post
    Thank you for responding but would the first answer not be 0.2 * 0.1 using that logic? That is 20% of the sharpeners have the defect, and 10% of that 20% have the other defect?
    Yes, not reading the question carefully enough, and the second should be 0.2*0.9

    RonL
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