i) [7 Marks] Suppose that there are ten easy routes up a mountain and five

dififcult routes. A hiker has no idea which routes are easy and which are

difficult. She takes 6 hikes up the mountain, each time choosing a route at

random from the same 15 routes. Showing your reasoning, and the proba-

bility that the hiker will choose an easy route on at least 3 occasions. [Leave

your answer in unsimplied form]

ii) [8 Marks] An engineer purchases electronic components from a manufac-

turer. It is known that 50 percent of the components are defective. What

is the minimum number of components the manufacturer must purchase to

be at least 90 percent certain that she will obtain at least one non-defective

component? [An exact numerical answer is required

i) [7 Marks] Suppose that there are ten easy routes up a mountain and five difficult routes. A hiker has no idea which routes are easy and which are difficult. She takes 6 hikes up the mountain, each time choosing a route at random from the same 15 routes. Showing your reasoning, find the proba- bility that the hiker will choose an easy route on at least 3 occasions. Leave your answer in unsimplified form] ii) [8 Marks] An engineer purchases electronic components from a manufac turer. It is known that 50 percent of the components are defective. What is the minimum number of components the manufacturer must purchase to be at least 90 percent certain that she will obtain at least one non-defective component? An exact numerical answer is required]