Hi, Please can I have some help with problem. The following is a random experiment. A wafer from a semiconductor manufacturing is to be selected randomly and a location on the wafer inspected for contamination particles. The sample space for the number of contamination particles at the inspected location is S= {0, 1, 2, 3, 4, 5}. Relative frequencies for these outcomes are 0.4, 0.2, 0.15, 0.10, 0.05 and 0.10 respectively. Use relative as probabilities. Let A be the event that there are no contamination particles at the inspected location. Let B be the event that there are at most three contamination particles at the inspected location. Let C be the event that there are an odd number of contamination particles at the inspected location. 1- How many events are possible? 2- Find the probability of the following: - complement of A - B and C ( or B intersection C) For the first question: Total events =2^6 For the second question I have no idea. thank you B
First let's define A, B, and C using set notation: A = {0} B = {3, 4, 5} C = {1, 3, 5} The complement of A, A' = {1, 2, 3, 4, 5}, meaning there at least one particle. The probability of A', P(A') = 1 - P(A) = 0.6. B intersect C means including the events that occur in BOTH B and C, so... B and C = {3, 5}. P (B and C) = P(3) + P(5) = 0.2. Er, I just noticed the date on the original post, but hope this helps somebody anyway.
Let us define the individual spaces: A={0} B={0,1,2,3} (at most three contaminated particles} C={1,3,5} P(A)=0.4 Complement of A= 1-0.4 = 0.6 P(B intersection C) = P(B)P(C) = 0.3