Conditional Probability

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

Question 89

Medium

An ecological study analyzed 400 quadrats (sampling areas) in a nature reserve to record the presence of three rare plant species:

Alpine Saxifrage ( $A$ )
Bluebell ( $B$ )
Common Spotted Orchid ( $C$ )

The findings are summarized in the following table:

Species Presence	$A$	$B$	$C$	$A$ and $B$	$A$ and $C$	$B$ and $C$	All three
Number of quadrats	220	150	130	80	70	60	40

Represent this information by fully completing a Venn diagram. The region for Alpine Saxifrage only ( $A$ but not $B$ or $C$ ) has been pre-filled with the number 110.

[4]

A quadrat is selected at random from the study. Calculate the probability that the quadrat:

(i) contains Alpine Saxifrage only.

(ii) contains at least two of the three rare plant species.

(iii) contains Alpine Saxifrage or Bluebell or both, given that it does not contain the Common Spotted Orchid.

[6]

Determine whether the presence of Bluebells and the presence of Common Spotted Orchids are independent events. Fully justify your answer.

[3]

Conditional Probability

Question 89

Conditional Probability Questions

Conditional Probability

Question 89

Conditional Probability Questions