Question

Blood diamonds.According to Global Research News(March 4, 2014), one-fourth of all rough diamonds producedin the world are blood diamonds. (Any diamond that is mined in a war zone—often by children—to finance a warlord’s activity, an insurgency, or an invading army’s effort is considered a blood diamond.) Also, 90% of the world’s rough diamonds are processed in Surat, India, and, of these diamonds one-third are blood diamonds.

a.Find the probability that a rough diamond is not a blood diamond.

b.Find the probability that a rough diamond is processed in Surat and is a blood diamond.

Short answer

1. Probability (not a blood diamond) = ¾ = 75%
2. Probability of a Surat processed blood diamond = 29.7%

Step-by-step solution

 Step 1: Finding the probability that a rough diamond is not a blood diamond

$\begin{array}{rcl}\text{Roughdiamonds}& =& \text{Probability}\left(\text{blooddiamond}\right)+\text{Probability}\left(\text{notablooddiamond}\right)\\ \text{1}& =& \mathrm{¼}+\text{Probability}\left(\text{notablooddiamond}\right)\\ \text{Probability}\left(\text{notablooddiamond}\right)& =& \text{1}–\frac{1}{4}\\ \text{Probability}\left(\text{notablooddiamond}\right)& =& \frac{3}{4}\\ & & \end{array}$

Therefore, the probability of a diamond not being a blood diamond is 0.75

Calculating the probability of a blood diamond processed in Surat

P (A) = diamond processed in Surat

P (B) = Blood diamonds processed in Surat

$\begin{array}{l}\text{P}\left(\text{AandB}\right)\text{=P}\left(\text{A}\right)\text{×P}\left(\text{B}\right)\\ \text{=0.9×}\frac{1}{3}\\ \text{=0.297}\\ \end{array}$

Therefore, the probability of a diamond being a blood diamond and processed in Surat is 0.297.