Malenky Aviation operates commuter flights using aircraft that can take ten passengers.

During each flight passengers are given a hot drink and a ‘Snack Pack’ that contains a ham sandwich and a cake. The company is aware that some of their passengers may be vegetarians and therefore every flight is stocked with one vegetarian Snack Pack that contains a cheese sandwich in addition to ten that contain ham.

If 10 per cent of the population are vegetarians, what is the probability that on a fully booked flight there will be at least one vegetarian passenger who will be dissatisfied with their Snack Pack?