Answer to Question #219343 in Statistics and Probability for manu

Question

An item produced by a company is susceptible to two types

of defects namely, A and B. The probability that an item has defect A is 1/6. The probability that it has defect

B is 1/8 . Calculate the probability that the item has 

1. (i) Both A and B defects
2. (ii) Only defect A
3. (iii) Only defect B
4. (iv) One defect only
5. (v) At least one defect

Answer 1

1.(i) $P=\frac{1}{6}*\frac{1}{8}=\frac{1}{48}\approx0.0208.$

2.(ii) $P=\frac{1}{6}*(1-\frac{1}{8})=\frac{7}{48}\approx 0.1458.$

3(iii) $P=\frac{1}{8}*(1-\frac{1}{6})=\frac{5}{48}\approx0.1042.$

4(iv) $P=\frac{7}{48}+\frac{5}{48}=\frac{12}{48}=\frac{1}{4}=0.25.$

5.(v) $P=1-\frac{5}{6}*\frac{7}{8}=1-\frac{35}{48}=\frac{13}{48}\approx0.2708.$