The diagram shows a lucky draw spinner at a departmental store.
The pointer is equally likely to stop at any of the sectors.
The sectors show a GRAND prize, $5 or$10 prize vouchers to be won or a MISS.
Each customer at the store is entitled to 1 spin for every $50 spent.

1. Find the probability of landing on a GRAND sector.

There are $2$ GRAND sectors out of $8$ equal sectors.

$P(\text{GRAND})=\frac{2}{8}=\frac{1}{4}$

1. Find the probability of landing on a \$5 or \$10 voucher sector.

There are $3$ sectors labelled $5 and $2$ sectors labelled $10, out of $8$ equal sectors.

$P(\text{\$5 or \$10 voucher})=\frac{3+2}{8}=\frac{5}{8}$

1. Find the number of spins Mrs Singh gets.

Mrs Singh spends $\char36{}120$.

Since each spin is given for every $\char36{}50$ spent,
$120 \div 50 = 2\text{ remainder }20$
So Mrs Singh gets $2$ spins.

2. Find the probability that she wins at least one prize in 2 spins.

A prize means any sector except MISS.

For one spin,
$P(\text{MISS})=\frac{1}{8}$

So for 2 spins,
$P(\text{no prize in both spins})=\frac{1}{8}\times\frac{1}{8}=\frac{1}{64}$

Hence,
$P(\text{at least one prize})=1-\frac{1}{64}=\frac{63}{64}$