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