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2.3.3 Conditional probability (A-level only)

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Question 91

In a reliability study of an automated irrigation system, two specific failure modes are monitored:

EEE: the system experiences an electrical sensor failure. WWW: the system experiences a water pressure drop.

From historical maintenance data, it is found that:

P(E′∩W)=0.12andP(E′∩W′)=0.68 P(E' \cap W) = 0.12 \quad \text{and} \quad P(E' \cap W') = 0.68 P(E′∩W)=0.12andP(E′∩W′)=0.68
a.

Find P(E)P(E)P(E).

[2]
b.

Find P(E∪W)P(E \cup W)P(E∪W).

[1]
c.

Given that the probability of an electrical failure, given a water pressure drop, is P(E∣W)=0.4P(E|W) = 0.4P(E∣W)=0.4,

calculate P(E∩W)P(E \cap W)P(E∩W).

[3]
d.

Determine, with justification, whether the events EEE and WWW are independent.

[2]

2.3.3 Conditional probability (A-level only) Questions

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