Revision mid-term - Revision for Mid-term (Please do not...

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Revision for Mid-term (Please do not distribute) Question Of all the households in the UK, 40% have a plasma TV and 50% have a laptop computer. There are 25% of households that have both a plasma TV and a laptop. Find the probability that a household chosen at random has either a plasma TV or a laptop computer but not both. Solution Question There are 125 diners in a restaurant who were surveyed to find out if they had ordered garlic bread, beer or cheesecake. 15 diners had ordered all three items 43 diners had ordered garlic bread 40 diners had ordered beer 44 diners had ordered cheesecake 20 had ordered beer and cheesecake 26 had ordered garlic bread and cheesecake 25 had ordered garlic bread and beer. A diner is chosen at random. Find the probability that the diner ordered a all three items, 1
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b beer but not cheesecake and not garlic bread, c garlic bread and beer but not cheesecake, d none of these items. Solution Question Jean always goes to work by bus or takes a taxi. If one day she goes to work by bus, the probability she goes to work by taxi the next day is 0.4. If one day she goes to work by taxi, the probability she goes to work by bus the next day is 0.7. Given that Jean takes the bus to work on Monday, find the probability that she takes a taxi to work on Wednesday. Solution 2
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P(Taxi on Weds) =0.4×0.3+0.6×0.4 =0.36 3
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Somchai has two coins. One is fair, with a head on one side and a tail on the other. The second is a trick coin and has a tail on both sides. Somchai picks up one of the coins at random and flips it. a Find the probability that it lands heads up. b Given that it lands tails up, find the probability that he picked up the fair coin. Solution a. P(Head)=1/2 ×1/2 =1/4 b. P (Fair | Tail) = P(Fair and Tail) / P (Tail) = (1/2 × 1/2) / (1/2 × 1/2 + 1/2) = 1/3 Question An online readers’ club has 50 members. Glasses are worn by 15 members, 18 are left handed and 21 are female. There are four females who are left handed, three females who wear glasses and five members who wear glasses and are left handed. Only one member wears glasses, is left handed and female. 4
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Revision mid-term - Revision for Mid-term (Please do not...

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