Question:
A random variable X has the following probability distribution
\(X = x\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(P(X = x)\) \(0.15\) \(0.23\) \(0.10\) \(0.12\) \(0.20\) \(0.08\) \(0.07\) \(0.05\)
For the events \(E = \{X\text{ is a prime number}\}\), \(F = \{X < 4\}\), \(P(E\cup F)\) is
A random variable X has the following probability distribution
For the events \(E = \{X\text{ is a prime number}\}\), \(F = \{X < 4\}\), \(P(E\cup F)\) is
| \(X = x\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) |
| \(P(X = x)\) | \(0.15\) | \(0.23\) | \(0.10\) | \(0.12\) | \(0.20\) | \(0.08\) | \(0.07\) | \(0.05\) |
For the events \(E = \{X\text{ is a prime number}\}\), \(F = \{X < 4\}\), \(P(E\cup F)\) is
Show Hint
List the values in each event, add their probabilities and subtract the overlap.
Updated On: Oct 1, 2026
- \(0.5\)
- \(0.77\)
- \(0.35\)
- \(0.75\)
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
For two events, \(P(E \cup F) = P(E) + P(F) - P(E \cap F)\).
Step 2: Find the events.
\(E\) (prime numbers in 1 to 8): \(\{2, 3, 5, 7\}\). \(F\) (\(X < 4\)): \(\{1, 2, 3\}\). \(E\cap F = \{2, 3\}\).
Step 3: Add the probabilities.
\(P(E) = 0.23 + 0.10 + 0.20 + 0.07 = 0.60\).
\(P(F) = 0.15 + 0.23 + 0.10 = 0.48\).
\(P(E\cap F) = 0.23 + 0.10 = 0.33\).
Step 4: Combine.
\[ P(E\cup F) = 0.60 + 0.48 - 0.33 = 0.75 \]
Final Answer:
\(P(E\cup F) = 0.75\), option (D). \[ \boxed{0.75} \]
For two events, \(P(E \cup F) = P(E) + P(F) - P(E \cap F)\).
Step 2: Find the events.
\(E\) (prime numbers in 1 to 8): \(\{2, 3, 5, 7\}\). \(F\) (\(X < 4\)): \(\{1, 2, 3\}\). \(E\cap F = \{2, 3\}\).
Step 3: Add the probabilities.
\(P(E) = 0.23 + 0.10 + 0.20 + 0.07 = 0.60\).
\(P(F) = 0.15 + 0.23 + 0.10 = 0.48\).
\(P(E\cap F) = 0.23 + 0.10 = 0.33\).
Step 4: Combine.
\[ P(E\cup F) = 0.60 + 0.48 - 0.33 = 0.75 \]
Final Answer:
\(P(E\cup F) = 0.75\), option (D). \[ \boxed{0.75} \]
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