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2.3 Probability

2.3 Probability

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Question 99

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 four regions within the circles and the region outside the circles.

[5]
Markscheme

2.3 Probability Questions

  1. A Level
  2. /Maths
  3. /2.3 Probability

200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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