An overworked math professor is considering a combined life insurance/long-term disability policy that costs $550 for one year of coverage. The policy pays out $120,000 in the event of his death, and $20,000 if he survives but misses more than 6 months of work for medical reasons (called “long-term disability”).
Based on the professor’s profile, it is estimated that he has a .986 probability of surviving with no long-term disability, a .012 probability of surviving but with a long-term disability, and a .002 probability of not surviving the year at all.
(a) Construct a probability distribution for the discrete random variable X representing the net value of this policy to the insurance company.

The First answer is

VWXZ+VWXY+WYZ+VXY+VWZ+XYZ

The second possible answer is:

VWXZ+VWYZ+WYZ+VXY+VWZ+XYZ

Step-by-step explanation:

First we draw the k-maps for the function . There are two k-maps, one with V as zero while the other is V as 1. Then we combine the entries in power of 2. Remember that the function is given in maxterms form.Max-terms are those whose value is 0. So all the values other than max-values are either 1 or don't care. So we will keep these terms 0 and other as 1. The k-maps are attached in the files below. The essential prime implicants are those which are repeated in all the possible solutions.In this case Essential prime implicants are :

VWXZ+WYZ+VXY+VWZ+XYZ

http://www.32x8.com/sop5A-B-C-D-Em_4-5-7-8-10-14-15-16-17-18-21-22-23-31d_1-2-12-13option-0899788976571894282724?fbclid=IwAR2BaNgaMe0FXK1AEcwzLb1tkw5Oo-DIn-w0QNxE6ck9nYOSS1GnGtWC4SU