[Math] Finding the probability of a randomly selected event

probabilityrandom variablesstatistics

I know I'm over-thinking the following question, I just need to know how to start!

In a certain population of women 4% develop symptoms of a classic disease, 20% are smokers, and 3% are smokers and have developed the symptoms of the disease.
a) Find the probability that a randomly selected woman from this population has developed symptoms of the disease, or is a smoker, or both.
b) Find the probability that a randomly selected woman from this population is not a smoker and has not developed symptoms of the disease.

Please help! Thank you.

Best Answer

Hints:

  • Probability of union of event: $P(A\cup B) = P(A)+P(B)-P(A\cap B)$
  • The probability of the complement of an event: $P(A^c) = 1-P(A)$
  • DeMorgan's formula: $(A \cup B)^c = A^c \cap B^c$
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