Suppose 80% of kids who visit a doctor have a fever, and 30% of kids with a fever have sore throats. What's the probability that a kid who goes to the doctor has a fever and a sore throat? Round to three decimal places.
thats wrong
To find the probability that a kid who goes to the doctor has a fever and a sore throat, we can use conditional probability.
Let's denote:
A = Kid has a fever
B = Kid has a sore throat
We are given the following probabilities:
P(A) = 0.80 (80% of kids have a fever)
P(B|A) = 0.30 (30% of kids with a fever have a sore throat)
We want to find P(A and B), which means the probability that a kid has both a fever and a sore throat.
The formula for conditional probability is:
P(A and B) = P(A) * P(B|A)
Substituting the given probabilities into the formula:
P(A and B) = 0.80 * 0.30
Calculating the result:
P(A and B) = 0.24
Therefore, the probability that a kid who goes to the doctor has both a fever and a sore throat is 0.240 (rounded to three decimal places).
F=fever
S=sore throat
P(F)=80%
P(S|F)=30%
But
P(S|F)=P(S∩F)/P(F)
P(S∩F)=P(S|F)*P(F)=30%*80%=0.24