14 5. Asha, Davinda and Jerry each have a bag containing a large number of counters, some of which are white and the rest are red. Each person draws counters from their bag one at a time, notes the colour of the counter and returns it to their bag. The probability of Asha getting a red counter on any one draw is 0.07 (a) Find the probability that Asha will draw at least 3 white counters before a red counter is drawn. (2) (b) Find the probability that Asha gets a red counter for the second time on her 9th draw. (2) The probability of Davinda getting a red counter on any one draw is p. Davinda draws counters until she gets n red counters. The random variable D is the number of counters Davinda draws. Given that the mean and the standard deviation of D are 4400 and 660 respectively, (c) find the value of p. (4) Jerry believes that his bag contains a smaller proportion of red counters than Asha’s bag. To test his belief, Jerry draws counters from his bag until he gets a red counter. Jerry defines the random variable J to be the number of counters drawn up to and including the first red counter. (d) Stating your hypotheses clearly and using a 10% level of significance, find the critical region for this test. (5) Jerry gets a red counter for the first time on his 34th draw. (e) Giving a reason for your answer, state whether or not there is evidence that Jerry’s bag contains a smaller proportion of red counters than Asha’s bag. (2) Given that the probability of Jerry getting a red counter on any one draw is 0.011 (f) show that the power of the test is 0.702 to 3 significant figures. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________