In: Statistics and Probability
In a doctor's waiting room, the probability of a patient having a fever (F) is 0.25, the probability of a patient having nausea (N) is 0.15, and the probability of a patient having both conditions is 0.10 Answer these questions : (results to two decimal places) to. What is the probability that a patient is not nauseated? b. What is the probability that a patient does not have any of the conditions? c. What is the probability that a patient will be nauseated given that they have a fever? d. Are the events of "fever" and "nausea" independent? Yes or no. Explain. and. Are the events of "fever" and "nausea" mutually exclusive? Yes or no. Explain.
Dear student, please comment in the case of any doubt and I would love to clarify it.
P(A) = n(E)/n(S)
Where P(A) is the probability of an event A
n(E) is the number of favorable outcomes
n(S) is the total number of events in the sample space.
a)
Probability of a patient having nausea = 0.15.
probability of a patient having only nausea = 0.15 - 0.10(of both) = 0.05
So the probability of a patient not having nausea = 1 - 0.05 = 0.95
b)
Probability of a patient having both = 0.10
Probability of a patient having only fever = 0.15
Probability of a patient having only nausea = 0.05
So the probability of a patient not having both= 1 - (0.10 + 0.15 + 0.05) = 0.70
c)
The probability that a patient will be nauseated knowing that they have a fever = probability of having both = 0.10
d)
Fever and Nausea are interdependent as they do not have any relation, any person can have nausea, it doesn't mean he had a fever as well, there is no correlation between them.
They are mutually exclusive as the sum of their probabilities is 1, which is what mutually exclusive is.
I have drawn a Venn diagram for the question, please refer to it.