The following shows the results of a survey on the types of exercise taken by a group of 100 people - Edexcel - A-Level Maths: Statistics - Question 6 - 2012 - Paper 1

To find the probability of a person taking none of these exercises:

1. First calculate the total number of people involved in the exercises:

   • Total from the diagram = 100
   • Total participants in exercises = 100 - (15 + 3 + 20 + 15 + 10 + 5 + 25) = 7

2. The probability that a randomly selected person takes none of these exercises is: $P(None) = \frac{7}{100} = 0.07$

To find the probability that a randomly selected person swims but does not run:

1. Identify those who swim but do not run:

   • Only Swim = 3 + Swim & Cycle (5) = 8

2. Therefore, the probability is: $P(Swim \text{ and not Run}) = \frac{8}{100} = 0.08$

To find the probability that a randomly selected person takes at least two different types of exercise:

1. Identify people engaged in at least two types:

   • Run & Swim only: 15
   • Swim & Cycle only: 5
   • Run & Cycle only: 10
   • All three: 25
   • Total = 15 + 5 + 10 + 25 = 55

2. The probability is: $P(At \ least \ 2) = \frac{55}{100} = 0.55$

To find the probability that Jason swims but does not cycle, given that he runs:

1. Given Jason runs, the relevant groups become:

   • Those who run = 65
   • Among them, those who swim but do not cycle = 15 (Run & Swim only) + 25 (All three) = 40 are swimming.

2. The conditional probability is: $P(Swim \text{ and not Cycle } | Run) = \frac{40}{65} = \frac{8}{13}$