Question about probability of being a heterozygous carrier, GENETICS QUESTION

Question

A 26-year-old woman of Norwegian descent seeks genetic counseling. Her brother died at age eight of documented cystic fibrosis. Both of their parents are deceased. The woman undergoes DNA testing for 70 CF mutations which collectively detects approximately 90% of CF carriers of northern European descent. Testing reveals that she is negative for all 70 mutations. What is the probability that she is a heterozygous carrier of CF?

So, my reasoning is that to be a heterozygous carrier, she has to have a 2/3 chance X by the 10% out of the mutations that weren't detected. I got 1/15, however the correct answer is 1/6. Please what am I missing ?

Answer 1

I have recorded and attached a video explaining the answer. Hope this helps!