During the 2014-2015 flu season 60% of children ages 6 months to 17 years receiv

Question

During the 2014-2015 flu season 60% of children ages 6 months to 17 years received the flu vaccine. During that time, 51% of children ages 6 months to 17 years were male. Also during that time, 19.6% were females that did not receive the flu vaccine. If a child between the ages of 6 months and 17 years is randomly selected, calculate the following probabilities. (give your answer as a percentage)

What is the probability of selecting a male that has not been vaccinated?

What is the probability of selecting a female that has been vaccinated?

What is the probability of selecting a male that has been vaccinated?

What is the probability of selecting a male or a child that has been vaccinated?

Explanation / Answer

Here, we are given that:

P( vaccine ) = 0.60
P( male ) = 0.51
P( female and no vaccine ) = 0.196

This is converted to a contingency table as:

Now using this the various probabilities here are computed as:

a) P( male and no vaccine ) = 0.204
b) P( female and vaccine ) = 0.294
c) P( male and vaccine ) = 0.306
d) P( male or vaccine ) = 1 - P( female and no vaccine ) = 1 - 0.196 = 0.804

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