A survey aims to identify the preference of different age groups for movie viewing in a theatre (for the first time) instead of downloading via a streaming service. Respondents were asked for their age and their preference. The results of the survey are tabulated below:

	Preference
Age (years)	Low	High	Undecided	Total
< 25	10	5	10	25
25 to 40	25	40	50	115
> 40	5	0	30	35
Total	40	45	90	175

SHOW YOUR WORKING and give your final answer as a fraction AND as a decimal (correct to two decimal places).

a) What is the probability that a respondent has an undecided preference for viewing a movie in a theatre?

b) What is the probability that a respondent has a high preference for viewing a movie in a theatre and is between 25 & 40 years old?

c) What is the probability that a respondent has a low preference for viewing a movie in theatre or is less than 25 years old?

d) Are the events "undecided preference" and "less than 25 years old" mutually exclusive. Briefly explain the reasoning behind your answer.