Question

A manufacturer of face masks has three factories A, E, L. Factor\ A produces 35% of the face masks, factor\ E produces 20% of the face masks, and factor\ L produces 45% of the face masks. Fift\-five percent of the face masks produced in factor\ A are N95 face masks, 45% of the face masks produced in factor\ E are N95 face masks and 15% of the face masks produced in factor\ L are N95 face masks. If a face mask manufactured b\ one these factories is selected at random, what is the probabilit\ that the face mask will be a N95 face mask?

Answer 1

Let the event of the mask produced in factory A be represented by A

Let the event of the mask produced in factory E be represented by E

Let the event of the mask produced in factory L be represented by L

Let the event of the mask is an N95 mask be N

Then we have:

P(A) = 0.35

P(E) = 0.20

P(L) = 0.45

P(N/A) = 0.55

P(N/E) = 0.45

P(N/L) = 0.15

We need to find the probability P(N)

P(N) = P(N/A) * P(A) + P(N/E) * P(E) + P(N/L) * P(L)

= 0.55 * 0.35 +0.45*0.20+0.15*0.45

= 0.35

= 35%

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!