Question 5 (20 Marks) 5.1 What is the probability that a fair coin lands Tails 8

Question

Question 5 (20 Marks) 5.1 What is the probability that a fair coin lands Tails 8 times in a row? (1 mark) 5.2 Three coins are tossed a List the elements in the sample space. b) Fid the probability that exactly two heads show (3 marks) 5.3 Find the probability that a 6 is obtained on one of the dice in a throw of two dice, given that the sum of the digits on the upper faces is 7, (4 marks) 5.4 On the weekend at a shopping complex food plaza, 65% of the customers buy lunch. Of those who buy lunch, 20% also buy ice cream for a dessert. Of those who do not buy lunch, 55% buy ice cream for a dessert. a What is the probability that a randomly selected customer does not buy ice cream, given that the customer does not buy lunch? b What is the probability that a randomly selected customer buys ice cream? (4 marks) From a deck of 52 cards, two cards are drawn without replacement. Find the following probabilities. a) The second card is a black 10, given that the first is red. 5.5 b) The second card is an ace, given that the first is also an ace c) A king and a 5 are drawn. d Two red cards are drawn. (8 marks)

Explanation / Answer

5.1 0.5 ^ 8 = 0.00390625

5.2 a) TTT,TTH,THT,THH,HTT,HTH,HHT,HHH

     b) 3/8 = 0.375

5.3 upper face is 7 = 4,3 2,5 1 6 4,3 2,5 1 6
     Probability of 6 when sum is 7 = 6/36 * 2/6 = 1/18

5.4 100 customers

     45 don't buy lunch
     55% of 45 buy ice cream = 24.75
     a) 24.75/100 = 0.2475

     b) 20% of 65 % buy ice cream = 13
         55% of 45 buy ice cream = 24.75
         Buy ice creams = 37.75
         probability = 0.3775

5.5   a) Red cards = 13
         Probability of getting red = 13/52
         Probability of black 10 = 2/51
         Total probability = (13/52) * (2/51) = 0.0098

       b) Ace card = 4
          Probability of ace = 4/52
          Probalility of 2nd ace = 3/51
          Total probability = (4/52) * (3/51) = 0.0045

       c) Number of King = 4
           Number of 5 = 5
           it happens in two ways:

           1st- king 2nd = 5     1st = 5 2nd = king

           (4/52) * (4/51) +   (4/52) * (4/51)

         d) Two red cards
              1st Red 2nd red

               Probaility = 26/52 * 25/51
    

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