Question

According to a​ study,

one dash fourthone-fourth

of all rough diamonds produced in one region are blood diamonds.​ Also,

7878​%

of the​ region's rough diamonds are processed in City​ X, and of these​ diamonds,

one dash thirdone-third

are blood diamonds.

a. Find the probability that a rough diamond produced in this region is not a blood diamond.

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

Answer 1

let B be the event that the diamond is blood diamond, R be the event that the diamond is rough diamond and C be event that the diamond is processed is city x

It is given that P(B|R) = 1/4, P(C) = 0.78 and P(B|C) = 1/3

(A) we have to find probability that a rough diamond produced in the regio is not a blood diamond

i.e. P(not B)

we know that P(not A) = 1-P(A) for an event A

so, we get

P(not B) =1-P(B) = 1-(1/4) = 3/4 or 0.75

So, required probability is 0.75

(B) We have to find the probability of P(B and C)

we know the formula P(B and C) = P(B)*P(B|C)

where P(B) = 0.78 and P(B|C) = 1/3 or 0.33

Setting the values, we get

P(B and C) = 0.78*0.33 = 0.26

So, required probability = 0.26