SOLUTION: About 3% of children in a country are allergic to peanuts. Choose three children at random and let the random variable X be the number in this sample who are allergic to peanuts. T

Question 1153531: About 3% of children in a country are allergic to peanuts. Choose three children at random and let the random variable X be the number in this sample who are allergic to peanuts. The possible values X can take are 0, 1, 2, and 3. What is the conditional probability that exactly two of the children will be allergic to peanuts, given that at least one of the three children suffers from this allergy? (Round your answer to four decimal places.)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
probability from 3
0: .97^3=0.91267
1: 3(.97^2)(0.03)=0.08468
2: 3(.97)(.03^2)=0.00262
3: .03^3=0.00003
given that at least 1 has it (prob. 0.08733) probability exactly 2 have it is 0.00262/0.08468 or 0.0309
RELATED QUESTIONS
A recent study reports that 2.5% of elementary children are allergic to peanuts. A random (answered by stanbon)

A recent study reports that 2.5% of elementary children are allergic to peanuts. A random (answered by stanbon)

assume there is a 4 person family and you are looking at the gender of the children. let... (answered by Fombitz)

The literacy rate for a nation measures the proportion of people age 15 and over that can (answered by Boreal)

The random variable x represents the number of boys in a family of three children.... (answered by Fombitz)

The random variable x represents the number of boys in a family of three children.... (answered by khwang)

Let the random variable x represent the number of girls in a family with three children.... (answered by robertb)

Census data are often used to obtain probability distributions for various random... (answered by ewatrrr)

The random variable x represents the number of boys in a family of three children.... (answered by stanbon)