Question

Seventy percent of children who go to the doctor have fevers. Of those with fevers, 30% also have a rash. Of those without fevers, 20% have a rash. What is the probability that a child at the doctor's office with a rash does not have a fever

Answer 1

Answer:

The probability that a child with a rash does not have a fever is 22%

Step-by-step explanation:

1. Probability of having fever:

$P(fever)=0.70$

2. Probability of not having fever:

$P(not fever)=1-P(fever)\\P(not fever)=1-0.70\\P(not fever)=0.30$

3. Probability of fave fevers and a rash:

$P(fever and rash)=(0.70)(0.30)=0.21$

4. Probability of having a rash but not a fever:

$P(rash and not fever)=(0.30)(0.20)=0.60$

5. Probability of having a rash:

$P(rash)=P(rash and fever)+P(rash and no fever)\\P(rash)=0.21+0.06=0.27$

6. Probability a child with a rash does not have a fever

$P=\frac{P(rash and not fever)}{P(rash)} =\frac{0.06}{0.27} =0.22$

22% of the child at the doctor's office with a rash does not have a fever.