1.1. State the conditions that must be satisfied to be able to model a random variable $X$ with a binomial distribution $B(n,p)$.

1.2. A fair spinner has 8 sectors labelled with the numbers 1 through 8. For each of the following cases, state with a reason whether or not a binomial distribution would be appropriate for modelling the specified random variable.

(i) The random variable $S$ is the number of the sector that the spinner lands on when it is spun.

(ii) The random variable $W$ is the number of times the spinner is spun until it lands on ‘7’ for the first time.

(iii) The random variable $Y$ is the number of times the spinner lands on a prime number when it is spun twelve times.

(iv) On the first spin, it is a ‘win’ if the spinner lands on an even number. On subsequent spins it is a ‘win’ if the spinner lands either on the same number as the previous spin or on a factor of the number from the previous spin.  The random variable   $L$ is the number of wins when the spinner is spun ten times.

1.3. For the random variable $W$ defined in (b)(ii) above, give the name of the probability distribution that would be appropriate for modelling $W$.