- 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
- Find the probability that Asha will draw at least 3 white counters before a red counter is drawn.
- Find the probability that Asha gets a red counter for the second time on her 9th draw.
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,
- find the value of \(p\).
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.
- Stating your hypotheses clearly and using a \(10 \%\) level of significance, find the critical region for this test.
Jerry gets a red counter for the first time on his 34th draw.
- 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.
Given that the probability of Jerry getting a red counter on any one draw is 0.011
- show that the power of the test is 0.702 to 3 significant figures.