Question

A random variable X has the following probability distribution:

X :	1	2	3	4	5	6	7	8
P (X) :	0.15	0.23	0.12	0.10	0.20	0.08	0.07	0.05

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

Options

•  0.50

•  0.77

• 0.35

• 0.87

   

Answer 1

0.77
 
E = { X is a prime number}  = {2, 3, 5, 7}

\[P\left( E \right) = P\left( 2 \right) + P\left( 3 \right) + P\left( 5 \right) + P\left( 7 \right) = 0 . 62\]
F = {X < 4} = {X = 1, 2, 3} 
\[P\left( F \right) = P\left( 1 \right) + P\left( 2 \right) + P\left( 3 \right) = 0 . 5\]
\[\text{ Now } , \]
\[E \cap F =  {2, 3}  \]
\[P\left( E \cap F \right) = P\left( 2 \right) + P\left( 3 \right) = 0 . 35\]
\[P\left( E \cup F \right) = P\left( E \right) + P\left( F \right) - P\left( E \cap F \right) = 0 . 62 + 0 . 50 - 0 . 35 = 0 . 77\]