Question

BMI (5.2) Suppose we select two American young women in this age group at random. Find the probability that at least one of them is classified as underweight. Show your work.

Short answer

P (at least one of two underweight) = $0.245$

Step-by-step solution

Step 1. Given Information

$\mu =26.8\sigma =7.4$

Step 2. Concept used

Using complement rule: $P(notA)=1-P\left(A\right)$

Step 3. Calculation

$P\left(underweight\right)=0.131$

Complement rule: $P(notA)=1-P\left(A\right)$

Applying the complement rule, the likelihood of not being underweight is as follows:$P(notunderweight)=1-P\left(underweight\right)=1-0.131=0.869=86.9\%$

Rule of multiplication (if occurrences A and B are unrelated):

$P(twonotunderweight)=P(notunderweight)\times P(notunderweight)=0.869\times 0.869=0.755$

Use the complement rule once more:

$P(atleastoneoftwounderweight)=1-P(twonotunderweight)=1-0.755=0.245$