(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In a population of children 60% are vaccinated against the 'waterpokken'. The probablilities of contracting 'waterpokking' are 1/1000 if the child is vaccinated and 1/100 if not.

a: Find the probability that a child selected at random will contract 'waterpokken'.

2. Relevant equations

Bayes Theorem: P(A|B) = P(A/\B) / P(B)

Formula sheet? View attachment stat_formulas.pdf

3. The attempt at a solution

Known values: P(V) = 0.6 | P(⌐V) = 0.4 | P(W|V) = 0.001 | P(W|⌐V) = 0.01

a: Find the probability that a child selected at random will contract 'waterpokken'.

- The question is: what is P(W)?

From Bayes Theorem I conclude: P(W) = P(V/\W) / P(V|W)

Both P(V/\W) & P(V|W) are unkown at this stage.

- P(V/\W)?

Fill in known values in bayes theorem:

P(W|V) = P(W/\V) / P(V) = 0.001 = P(W/\V) / 0.6

So: P(V/\W) = P(W/\V) = P(V) * P(W|V) = 0.6 * 0.001 = 0.0006

Until here I get it! But now...

- P(V|W)?

P(V|W) = P(V/\W) / P(W) but I don't know P(W) :S?

Answer sheet solution:

P(W/\⌐V) = P(W|⌐V) = 0.01 * 0.4 = 0.004

P(W) = P(W/\V) + P(W/\⌐V) = 0.0006 + 0.004 = 0.0046

1. What rules are applied in the third section? Could someone explain to me how they conclude to

P(W/\⌐V) = P(W|⌐V) and P(W) = P(W/\V) + P(W/\⌐V) ?

Maybe it's part of the formulas at the bottom of the first page of my formula sheet View attachment stat_formulas.pdf

2. Is there a way I could have known that I would need to work to that solution. Because I concluded I needed to work towards P(W) = P(V/\W) / P(V|W) but that plainly doesn't work..:(

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Probability Question

**Physics Forums | Science Articles, Homework Help, Discussion**