Explanation
To find the probability P(E∪F), we can identify the outcomes that belong to event E, event F, or both, and sum their corresponding probabilities. Alternatively, we can use the addition theorem of probability:
P(E∪F)=P(E)+P(F)−P(E∩F)
Let's break down the problem step-by-step using the set-compositions.
Step 1: Identify Elements and Probability of Event E
Event E consists of all values of X that are prime numbers between 1 and 8.
Let's calculate P(E):
P(E)=P(X=2)+P(X=3)+P(X=5)+P(X=7)
P(E)=0.23+0.12+0.20+0.07=0.62
Step 2: Identify Elements and Probability of Event F
Event F consists of all values of X that are strictly less than 4.
Let's calculate P(F):
P(F)=P(X=1)+P(X=2)+P(X=3)
P(F)=0.15+0.23+0.12=0.50
Step 3: Identify Elements and Probability of Intersection E∩F
The intersection event E∩F contains elements that are common to both sets E and F.
Let's calculate P(E∩F):
P(E∩F)=P(X=2)+P(X=3)
P(E∩F)=0.23+0.12=0.35
Step 4: Apply the Addition Formula
Now, substitute the values into the probability addition formula:
P(E∪F)=P(E)+P(F)−P(E∩F)
P(E∪F)=0.62+0.50−0.35
P(E∪F)=1.12−0.35=0.77
