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:
[tex]P(fever)=0.70[/tex]
2. Probability of not having fever:
[tex]P(not fever)=1-P(fever)\\P(not fever)=1-0.70\\P(not fever)=0.30[/tex]
3. Probability of fave fevers and a rash:
[tex]P(fever and rash)=(0.70)(0.30)=0.21[/tex]
4. Probability of having a rash but not a fever:
[tex]P(rash and not fever)=(0.30)(0.20)=0.60[/tex]
5. Probability of having a rash:
[tex]P(rash)=P(rash and fever)+P(rash and no fever)\\P(rash)=0.21+0.06=0.27[/tex]
6. Probability a child with a rash does not have a fever
[tex]P=\frac{P(rash and not fever)}{P(rash)} =\frac{0.06}{0.27} =0.22[/tex]
22% of the child at the doctor's office with a rash does not have a fever.
