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There are 200 students at a sports academy following a training program. Students can choose to participate in three specific workshops:

115 participate in Nutrition ( $N$ ),
85 participate in Psychology ( $P$ ),
90 participate in Bio-mechanics ( $B$ ),
40 participate in Nutrition and Psychology,
30 participate in Psychology and Bio-mechanics,
45 participate in Nutrition and Bio-mechanics,
10 participate in all three workshops.

Draw a Venn diagram to represent this information.

[4]

A student is selected at random from the program. Find the probability that this student participates in:

none of the three workshops,

[2]

Bio-mechanics only.

[2]

Students who want to specialize in high-performance coaching participate in both Psychology and Bio-mechanics. Given that a randomly chosen student wants to specialize in high-performance coaching,

find the probability that this student participates in all three workshops.

[2]

Conditional Probability Questions

Practise Edexcel A Level Maths Conditional Probability with exam-style questions for A Level Maths. 100 questions covering Set Notation, Conditional Probability, Conditional Probabilities in Venn Diagrams, Probability Formulae, and Tree Diagrams, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.