Maths paper soon help

zanharjabir

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  • Oct 28, 2007
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    A supermarket chain is running a promotion called Lucky Shopper in the hope of attracting larger numbers of customers. Each day 1000 customer cash register dockets spread randomly across the supermarket chain are printed with a three digit number between 000 and 999. Each morning before trading commences a Lucky Docket number is generated. Each of the digits in the Lucky Docket number is generated randomly from the numbers between 0 and 9, independently of the other two digits.

    a. What is the probability that the winning Lucky Docket number is 321?

    b. What is the probability of a Lucky Shopper winning the lottery?

    c. What is the probability that the winning number contains no 7s?

    d. What is the probability that the winning number contains at least one 7?
     

    zanharjabir

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  • Oct 28, 2007
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    The HR Manager at the Box Hill branch of the supermarket chain has identified seven women and 5 men who are qualified from amongst the staff who applied for six different Trainee Manager positions that are to be filled.

    a. How many different groups of qualified applicants can be selected for the positions?

    b. How many of those groups consist entirely of women?

    c. If the HR Manager selects the Trainee Managers by drawing their names at random out of a hat, what is the probability that the group of Trainee Managers will consist entirely of women?
     

    zanharjabir

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  • Oct 28, 2007
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    3. Two employees are selected at random from the Grocery Department which is staffed by 8 women and 12 men. Consider the following events.

    A = {the 1st person is a woman}

    B = {the 2nd person is a woman}

    C = {the 1st person is a woman and the 2nd person is a man}

    D = {the 1st person is a man and the 2nd person is a woman}

    E = {exactly one of the two people selected is a woman}

    a. Find P(A), P(B) and P(B/A)
    b. Are A and B independent?
    c. Are A and B mutually exclusive?
    d. Find P(C) and P(D)
    e. How is E related to C and D
    f. Find P(E)
     

    zanharjabir

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  • Oct 28, 2007
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    Seven cards labelled A, B, C, D, E, F, G are thoroughly shuffled and then dealt face upwards. Find the probabilities, giving each in its fractional form i.e. 1/n, of the following outcomes of the deal.

    a. The first three cards to appear are labelled, A, B, C in that order.

    b. The first three cards to appear are labelled, A, B, C but in any order.

    c. The seven cards appear in their original order: A, B, C, D, E, F, G.
     

    zanharjabir

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  • Oct 28, 2007
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    Seven cards labelled A, B, C, D, E, F, G are thoroughly shuffled and then dealt face upwards. Find the probabilities, giving each in its fractional form i.e. 1/n, of the following outcomes of the deal.

    a. The first three cards to appear are labelled, A, B, C in that order.

    b. The first three cards to appear are labelled, A, B, C but in any order.

    c. The seven cards appear in their original order: A, B, C, D, E, F, G.
     

    zanharjabir

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  • Oct 28, 2007
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    A student returns to his apartment late at night to find that the exterior lights have been put out. He can’t see the 5 keys on his key-ring to distinguish one from the other and thus cannot identify his front door key. He feels for the lock and then randomly chooses a key and tries it in the lock. The darkness is so deep that he must randomly choose a key each time, with no guarantee that the same key will not be picked again, and he continues doing this until he picks the correct key.

    a. What is the probability that he picks the correct key on the first try?

    b. What is the probability that the first 5 tries are all wrong?
     

    cbpower

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    Jun 20, 2008
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    zanharjabir said:
    A supermarket chain is running a promotion called Lucky Shopper in the hope of attracting larger numbers of customers. Each day 1000 customer cash register dockets spread randomly across the supermarket chain are printed with a three digit number between 000 and 999. Each morning before trading commences a Lucky Docket number is generated. Each of the digits in the Lucky Docket number is generated randomly from the numbers between 0 and 9, independently of the other two digits.

    a. What is the probability that the winning Lucky Docket number is 321?

    b. What is the probability of a Lucky Shopper winning the lottery?

    c. What is the probability that the winning number contains no 7s?

    d. What is the probability that the winning number contains at least one 7?

    MyAnswers :)
    a) Probability of getting 3 the first no- 1/10
    Probability of getting 2 as the second no- 1/10
    Probability of getting 1 as the third no-1/10

    So the probability of getting 321= 1/10 * 1/10 * 1/10 = (1/10)^3 = 1/1000
    (Method used- tree diagram)

    b) 1/1000 (only 1 customer will get the no assuming the no will not repeat for a day)

    c) 1st, 2nd and 3rd Digits should not have 7s.
    So the probability is 9/10 * 9/10 * 9/10 = (9/10 )^3=729/1000

    d) you will get 7s when -
    1st digit is 7 (Assume other digits are not 7s)
    2nd digit is 7 (Assume " " " " )
    3rd digit is 7 (Assume " " " " )
    Also 1 st & 2nd digits are 7, 2nd and 3rd digits are 7, 1st & 3rd digits are 7 or all digits are 7.

    So there are seven (7) possibilities of getting 7
    So the probability is = 7/1000
     
    Last edited:

    blastxp

    Junior member
  • Jul 8, 2007
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    koi ekath ekai bari welawata mokekwath ne mamath ookata answer hoyanawa
    here is the answer for 1 Q
    • Since the number is selected independently of the others 111 is a valid number. Also I am assuming that 123 is different form 321

    There are 10 number to pick from (0, 1, ... 9)
    There are 3 digits
    So
    10 ways to pick the first
    10 ways to pick the second
    10 ways to pick the third

    There is 1 way to pick 321 out of 1000. So 1/1000

    b. Assuming that each number is different, no two customers can get 123.

    So 1000 customers 1000 numbers . The probability that some one wins is 1.

    How many ways can the first number not be 7 = 9
    How many ways can the 2nd number not be 7 = 9
    How many ways can the 3rd number not be 7 = 9
    So there are 9*9*9 / 1000 ways of not having the number have any sevens

    d) Prob that is has at least 1 seven is 1 - P( no sevens) =

    1 - 9*9*9/1000
    yahoo answer eke dala thibba kalin
     

    madurax86

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    Jun 29, 2006
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    zanharjabir said:
    The HR Manager at the Box Hill branch of the supermarket chain has identified seven women and 5 men who are qualified from amongst the staff who applied for six different Trainee Manager positions that are to be filled.

    a. How many different groups of qualified applicants can be selected for the positions?

    b. How many of those groups consist entirely of women?

    c. If the HR Manager selects the Trainee Managers by drawing their names at random out of a hat, what is the probability that the group of Trainee Managers will consist entirely of women?

    not sure tho :P dont like probability or combinations
    but a bit sure tho ~
    a) number of people = 7+5=12
    the number of groups that can be made of any 6 identified people =12C6
    b)number of groups that will be entirely of women=7C6
    c)7C6/12C6