A random variable X has the following probability distribution: For the events E = {X: X is a prime number}, F = {X: X

Question

A random variable X has the following probability distribution: For the events E = {X: X is a prime number}, F = {X: X < 4}, the probability P (E ∪ F) is

Philoid · Accepted Answer

E=(X:X is a prime number)=(2,3,5,7)

P(E)=P(X=2)+(X=3)+(X=5)+(X=7)

P(E)=0.23+0.12+0.20+0.07=0.62

F=(X:X<4)=(1,2,3)

P(F)=P(X=1)+(X=2)+(X=3)

P(F)=0.15+0.23+0.12=0.5

E∩F=(X is a prime number as well as <4)=(2,3)

P(E∩F)=P(X=2)+P(X=3)

⇒ 0.23+0.12=0.35

P(E∪F)=P(E)+P(F)-P(E∩F)

⇒ 0.62+0.50-0.35

A random variable X has the following probability distribution:For the events E = {X: X is a prime number}, F = {X: X < 4}, the probability P (E ∪ F) is

A random variable X has the following probability distribution:

For the events E = {X: X is a prime number}, F = {X: X < 4}, the probability P (E ∪ F) is