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Question:
  1. a) Find the probability that a card chosen at random from the set of cards is
  • a Purple card.
  • a Blue card
  • a Orange or Green card
  • a Purple or Blue card
  • not a Blue card
  • a Red card

(b) Two cards are chosen at random one after another with replacement from the set of  
      cards, find the probability that

  • both are Orange
  • both are Blue
  • the first card is Purple and the second a Green
  • the first card is Orange and the second Blue
  • one is Blue and the other Green
  • one is Orange and the other Purple 

(c) Two cards are chosen at random one after another without replacement from the set
     of cards, find the probability that

  • both are Orange
  • both are Blue
  • the first card is Purple and the second a Green
  • the first card is Orange and the second Blue
  • one is Blue and the other Green
  • one is Orange and the other Purple 

(d) Three cards are drawn at random one after another without replacement from the
      set of cards, find the probability that

  • all are Blue
  • one Green, one Purple and one Orange

 Question 2 (30 marks)           

  • 300 students were asked if they go to school by bus or bicycle. Their responses are recorded in the table.

                                                Would marry in the next 3 years

 

Bus

Bicycle

Boy (B)

28

102

Girl (G)

152

18

If one student is selected at random from these 300 students, find the probability that
  • the student goes to school by bus; [2 marks]
  • the student is a boy;                                                 [2 marks]
  • the student is a girl who cycled to school; [2 marks]
  • the student is a boy and he goes to school by bus. [2 marks]
  • the student goes to school by bus given that the student is a girl.
                                                                            [2 marks]
  • the student is a boy given that the student goes to school by bicycle.

                                                                                                            [2 marks]

Given that a selected student is a boy, what is the probability that he goes to school by bus?                                                                                                        [2 marks] 

Are the events selecting a 'Boy' and go to school by 'Bicycle' independent? Explain.                                                                                                                     [2 marks]

Are the events selecting a 'Girl' and go to school by 'Bus' mutually exclusive? Explain.
                                                                                                                  [2 marks]

  • The probability that a student selected at random is a male is 0.48, and a student likes statistics is 0.35. The probability of a student selected at random is a female who likes statistics is 0.25.
  • Construct a contingency table based on the information given above.
                                                                                                                [4 marks]
  • What is the probability that a student selected at random is a male and likes statistics;             [2 marks]
  • What is the probability that a student selected at random is a female and dislikes statistics. [2 marks]
  • What is the probability that a student selected at random is a male or dislike statistics. [2 marks]
  • What is the probability that a student selected at random is a female or dislike statistics. [2 marks]

Question 3 (30 marks)

  • The bank manager expects a decline of 20% on customer fixed deposit in the current year. He introduced a scheme to monitor the decline. If the fixed deposit is heading for a decline, there is a 70% chance that the scheme will be negative. If the fixed deposit is not headed for a decline, there is 15% chance that the scheme will be negative. The manager randomly select a customer and the scheme shows negative. What is the probability that the bank will show a decline in fixed deposit?                                                                                                                              [10 marks] 
  • Given that 15% of the sale receipts at a departmental store is for electrical goods. If 5 receipts were selected, what is the probability that
    (i)     none is for electrical goods?                                                   [3 marks]    

           (ii)    3 are for electrical goods?                                                       [3 marks]        

           (iii)   at least 2 are for electrical goods?                                         [4 marks] 

  • A washing machine breaks down on an average of 3 times per year. Using the
     Poisson probability distribution formula, find the probability that during the next year        this washing machine will have
                       (i)       exactly 2 breakdowns;                                                   [5 marks]
                       (ii)     at most one breakdown.                                                [5 marks]
Answer:
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[Accessed 23 June 2024].

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