Skip to content

Course home

4.1 Probability (A-level only)

4.1 Probability (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145
Question 111

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]
Markscheme

4.1 Probability (A-level only) Questions

  1. A Level
  2. /Maths
  3. /4.1 Probability (A-level only)

164 exam-style questions on WJEC A Level Maths 4.1 Probability (A-level only), covering 4.1.1 Probability (A-level only), 4.1.2 Probability (A-level only), and 4.1.3 Probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank