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01. Q2 . A and B are two events such that P (A n B] = 0.1 P {A' r. 8'] =0.2 P {Bl =

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01. Q2 . A and B are two events such that P (A n B] = 0.1 P {A' r\". 8'] =0.2 P {Bl = 2PM] (a) Find PM} {4} [b] Find P {BM} {2} (c) Determine ifA and B are independent events. {1} (Total? marks} A teacher in a college asks her mathematics students what other subjects they are studying. She finds that, of her 24 students: 12 study physics 3 study geography 4 study geography and physics (a) A student is chosen at random from the class. Determine whether the event 'the student studies physics' and the event 'the student studies geography' are independent. {2} lb) It is known that for the whole college: 1 the probability of a student studying mathematics is 5 1 the probability of a student studying biology is 5 3 the probability of a student studying biology given that they study mathematics is 8 Calculate the probability that a student studies mathematics or biology or both. {4} (Total 6 marks] (13. A sample of 200 households was obtained from a small town. Each household was asked to complete a questionnaire about their purchases of takeaway food. A is the event that a household regularly purchases Indian takeaway food. Bis the event that a household regularly purchases Chinese takeaway food. it was observed that P(B|.-l} = 0.25 and PHIB) = 01 Of these households, 122 indicated that they did not regularly purchase Indian or Chinese takeaway food. A household is selected at random from those in the sample. Find the probability that the household regularly purchases both Indian and Chinese takeaway food. {Total 6 marks] Q4. A random sample of students aged between 16 and 21 years was asked their opinions regarding the level of the student loan available to students in higher education They were asked to comment on whether they feit the level of the loan was too low, about right or too high. The following table summarises their replies. Tun law Ahmt right. In high Age nf Ituant 16 1'Iyean 18 21 year: A student is chosen at random. Bis the event "the student is aged 1617 yea rs". C is the event "the student replied about right\". D is the event "the student replied too high". 3' is the event "not B\". D' is the event "not B". {3) Find: iii PlB " Cl: [ii] PID V B}; {1} {iii} PIC I Bi; {2} [iv] PID' U B']. {2' Bl {b} Define, in words as simply as possible, the event {0' U 3'}. Bl {Total 9 marks] (15. An |T help desk has three telephone stations: Alpha. Beta and Gamma. Each of these stations deals only with telephone enquiries. The probability that an enquiry is received at Alpha is 0.60. The probability that an enquiry is received at Beta is 0.25. The probability that an enquiry is received at Gamma is 0.15. Each enquiry is resolved at the station that receives the enquiry. The percentages of enquiries resolved within various times at each station are shown in the table. For example: 30 per cent of enquiries received at Alpha are resolved within 24 hours; 25 per cent of enquiries received at Alpha take between 1 hour and 24 hours to resolve. {a} {b} Find the probabilitv that an enquiry, selected at random, is: (El resolved at Gamma; {1} iii] resolved at Alpha within 1 hour; {1] {iii} resolved within 24 hours; {2} {iv} received at Beta, given that it is resolved within 24 hours. {3} A random sample of 3 enquiries was selected. Given that all 3 enquiries were resolved within 24 hours, calculate the probability that they were all received at: (ii Beta; {2} {ii} the same station. {4) {Total 13 marks} Q6. Alison is a member of a tenpin bowling club which meets at a bowling alley on Wednesday and Thursday evenings. The probability that she bowls on a Wednesday evening is 0.90. Independently, the probability that she bowls on a Thursday evening is 0.95. (a) Calculate the probability that, during a particular week, Alison bowls on: (i) two evenings; (ii) exactly one evening. (3) (b) David, a friend of Alison, is a member of the same club. The probability that he bowls on a Wednesday evening, given that Alison bowls on that evening, is 0.80. The probability that he bowls on a Wednesday evening, given that Alison does not bowl on that evening, is 0.15. The probability that he bowls on a Thursday evening, given that Alison bowls on that evening, is 1. The probability that he bowls on a Thursday evening, given that Alison does not bowl on that evening, is 0. Calculate the probability that, during a particular week: (i) Alison and David bowl on a Wednesday evening; (2) (ii) Alison and David bowl on both evenings; (2) (iii) Alison, but not David, bowls on a Thursday evening; (1) (iv) neither bowls on either evening. (3) (Total 11 marks)

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