Probability — Flashcards
Madhya Pradesh Board · Class 12 · Mathematics
50 flashcards for Probability (Madhya Pradesh Board Class 12 Mathematics) to test yourself on key terms and facts.
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यदि P(E ∩ F) = 1/8 and P(F) = 1/2. है तो सशर्त प्रायिकता ज्ञात कीजिए।
Answer
सशर्त प्रायिकता सूत्र का प्रयोग करें: P(E|F) = P(E ∩ F) / P(F) चरण 1: मानों को प्रतिस्थापित करें। P(E|F) = (1/8) / (1/2) चरण 2: व्युत्क्रम से गुणा करके भाग दें। P(E|F) = 1/8 × 2/1 = 1/4 उत्तर: P(E|F) …
Find the conditional probability if P(E ∩ F) = 1/8 and P(F) = 1/2.
Answer
Use the conditional probability formula: P(E|F) = P(E ∩ F) / P(F) Step 1: Substitute the values. P(E|F) = (1/8) / (1/2) Step 2: Divide by multiplying by the reciprocal. P(E|F) = 1/8 × 2/1 = 1/4 Answer…
A family has two children. Find the probability that both are boys given that at least one child is a boy.
Answer
Let E = both children are boys, and F = at least one child is a boy. Sample space: {(b,b), (g,b), (b,g), (g,g)} Step 1: Find P(F). F = {(b,b), (g,b), (b,g)} so P(F) = 3/4 Step 2: Find E ∩ F. E ∩ F = {…
एक परिवार में दो बच्चे हैं। यदि कम से कम एक बच्चा लड़का है तो दोनों के लड़का होने की प्रायिकता ज्ञात कीजिए।
Answer
मान लीजिए E = both children are boys, और F = at least one child is a boy. नमूना स्थान: {(b,b), (g,b), (b,g), (g,g)} चरण 1: P(F) ज्ञात कीजिए। F = {(b,b), (g,b), (b,g)} इसलिए P(F) = 3/4 चरण 2: E ∩ F ज्ञ…
1 से 10 तक के दस कार्ड एक बक्से में रखे हैं। एक कार्ड निकाला जाता है। यह देखते हुए कि संख्या 3 से बड़ी है, ज्ञात कीजिए कि यह सम होने की प्रायिकता क्या है।
Answer
मान लीजिए A = even number, B = number greater than 3. चरण 1: परिणामों की सूची बनाएं। A = {2,4,6,8,10} B = {4,5,6,7,8,9,10} A ∩ B = {4,6,8,10} चरण 2: प्रायिकताएँ ज्ञात करें। P(B) = 7/10 P(A ∩ B) = 4/10…
Ten cards numbered 1 to 10 are placed in a box. One card is drawn. Given that the number is greater than 3, find the probability that it is even.
Answer
Let A = even number, B = number greater than 3. Step 1: List outcomes. A = {2,4,6,8,10} B = {4,5,6,7,8,9,10} A ∩ B = {4,6,8,10} Step 2: Find probabilities. P(B) = 7/10 P(A ∩ B) = 4/10 Step 3: Apply co…
A die is thrown twice. Given that the sum is 6, find the probability that 4 has appeared at least once.
Answer
Let E = 4 appears at least once, and F = sum is 6. Step 1: List favourable outcomes for F. F = {(1,5), (2,4), (3,3), (4,2), (5,1)} So P(F) = 5/36 Step 2: Find E ∩ F. E ∩ F = {(2,4), (4,2)} So P(E ∩ F)…
एक पासे को दो बार फेंका जाता है। दिया गया है कि योगफल 6 है, तो प्रायिकता ज्ञात कीजिए कि 4 कम से कम एक बार आया हो।
Answer
मान लीजिए E = 4 appears at least once, और F = sum is 6. चरण 1: F के लिए अनुकूल परिणामों की सूची बनाएं। F = {(1,5), (2,4), (3,3), (4,2), (5,1)} तो P(F) = 5/36 चरण 2: E ∩ F ज्ञात कीजिए। E ∩ F = {(2,4), …
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