The document outlines a probability problem involving a sample space with five events and their associated probabilities. It calculates the probability of event e4, identifying that p(e4) equals 0.1. Additionally, it discusses the probability of event a, which includes events e1, e2, and e3.

1. A sample space S consists of five simple events with these probabilities:
P(E1) = P(E2) = .15 P(E3) = .4 P(E4) = 2P(E5)
a) Find the probability of the simple event E4 occurring? (Round to 1 decimal point)
b) Find the probability for even A occurring? (Round to 1 decimal point)
A = {E1, E2, E3}
Solution
a. P(E1) = P(E2) = .15 P(E3) = .4 P(E4) = 2P(E5) P(E1) + P(E2) + P(E3) +P(E4)
+2P(E4)=1 --> 0.15+0.15+0.4+3P(E4)=1 --> 0.7 +3P(E4)=1 --> 3P(E4)=1-0.7=0.3 -->
P(E4)=0.3/3=0.1