Originally Posted by

**c00ky** **Hi Guys, I have the following problem. Could anybody point explain to me how to solve this problem using probability trees?**

**Q) Companies A, B and C are producing nails. 30%, 45% and 25% of these nails are produced by companies A, B and C respectively. Quality checks reveal that 0.2%, 0.1% and 0.15% of this type of nails produced by companies A, B and C, respectively are defectives. **

**i) Construct a tree diagram for this question.**

**ii) What is the probability that a randomly chosen nail is produced by company A and is defective?**

**iii) What is the probability that a randomly chosen nail is defective?**

**iv) What is the probability that a randomly chosen nail is defective given that the nail is produced by company A?**

**v) What is the probability that a randomly chosen nail is produced by company A given that the nail is defective?**