6 A bank monitors the amounts of cash withdrawn from a cash machine. It categorises any withdrawal of an amount of \(\pounds 50\) or less as 'small' and any withdrawal of an amount greater than \(\pounds 50\) as 'large'. Over a long period of time the bank finds that the proportion of withdrawals that are small is 0.43 .
The bank wishes to model a sample of 10 withdrawals to examine the number of small withdrawals.

1. 1. State a suitable probability distribution for such a model, justifying your answer.
   2. State one assumption needed for the model to be valid.
2. 1. Find the probability that exactly 4 of the 10 withdrawals are small.
   2. Find the probability that exactly 4 of the 10 withdrawals are large.
   3. Find the probability that no more than 4 of the 10 withdrawals are large.
3. Find the probability that, in the 10 withdrawals, the 7th withdrawal is large and there are exactly 3 that are small.