Cars tested for roadworthiness. The main tyres, steering or bodywork. In total, 34
4 A garage keeps records of the last 94
reasons for failing the test are faulty
failed for tyres, 40 failed for steering and
29 failed for bodywork. 11 cars failed for
other reasons. 7 cars failed for both tyres
and steering, 6 for steering and bodywork
and 11 for bodywork and tyres. The
owner of the garage wishes to calculate
the number of cars that failed for all three
reasons.
a Draw a Venn diagram to represent
the information, using x to represent
the number of cars failing for all three
reasons.
b Hence calculate the value of x.
c Hence find the probability that a car
selected at random from this data set
failed for at least two reasons.