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2.3 Conditional Probabilities in Venn Diagrams

2.3 Conditional Probabilities in Venn Diagrams

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Question 15

In a survey of exotic plants in a botanical garden, the events S S\,S and F F\,F are defined as follows: S S\,S is the event that a plant is a succulent and F F\,F is the event that a plant is a flowering species. The probabilities are given by

P(S)=310P(S∪F)=2950 P(S) = \frac{3}{10} \quad P(S \cup F) = \frac{29}{50} P(S)=103​P(S∪F)=5029​

Given that S S\,S and F F\,F are independent,

a.

show that P(F)=25\displaystyle P(F) = \frac{2}{5}P(F)=52​

[4]
b.

The event X X\,X represents the plant belonging to a rare genus such that

P(X)=0.06P(S∩X)=P(X) P(X) = 0.06 \quad P(S \cap X) = P(X) P(X)=0.06P(S∩X)=P(X)

Find P(X′∣S)P(X' | S)P(X′∣S)

[2]
c.

Given that F F\,F and X X\,X are mutually exclusive,

draw a Venn diagram to represent the events SSS, FFF, and XXX, giving the exact probabilities of each of the five regions within the circles and the region outside the circles.

[5]
Markscheme

2.3 Conditional Probabilities in Venn Diagrams Questions

  1. A Level
  2. /Maths
  3. /2.3 Conditional Probabilities in Venn Diagrams

31 exam-style questions on Edexcel A Level Maths 2.3 Conditional Probabilities in Venn Diagrams. Each one has a worked solution and a mark scheme showing where the marks go.

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