# Thread: Probability of Australian nominates either cancer or heart disease but not both as m

1. ## Probability of Australian nominates either cancer or heart disease but not both as m

Hi there,

I've just started University level statistics and this question has me stumped:

A survey conducted by Roy Morgan Research asked 1116 people to
nominate health issues they consider most important. 60% of
respondents nominated cancer, and 29% mentioned heart disease.
Assume that these percentages are true for the population of
Australia and that 25% of all respondents nominated both cancer and
heart disease as most important health issues.

What is the probability that a randomly selected Australian
nominates either cancer or heart disease but not both as most
important health issues?

I'm finding the wording of the question difficult, i.e. what are
they asking us to find, is it the probability of C or H minus the
probability of C and H?

My attempt at the question is as follows: (please note that I'm
using the letter 'n' to represent the symbol 'and' and I'm using the
letter 'u' to represent the symbol 'or').

Let P (C) = Cancer
Let P (H) = Heart Disease

So am I trying to find, P (C u H) - P (C n H)?

P (C u H) = P (C) + P (H) - P (C n H) = 0.6 + 0.29 - 0.25 = 0.64

Therefore is the solution P (C u H) - P (C n H) = 0.64 - 0.25 = 0.39?

Thanks for any assistance

2. Yes, it's indeed asking for:

$P(C \cup H) - P(C \cap H)$