Probability Test 17
Bilingual timed test for SSC, RRB and Banking quant with clean Hindi, preserved math symbols and detailed solutions.
Probability Test 17
25 bilingual MCQs from Probability, including 5 fresh LearnAtMyPlace original supplemental questions with detailed solutions. Designed for cross-exam quantitative aptitude practice with preserved ₹, ×, %, ratios and Hindi wording.
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- Probability — Two-bag probability
1. Bag A has 5 red balls out of 11 balls. Bag B has 4 blue balls out of 13 balls. One ball is drawn from each bag. Find probability of red from A and blue from B. / Bag A में 11 में से 5 लाल गेंदें हैं। Bag B में 13 में से 4 नीली गेंदें हैं। हर bag से एक गेंद निकली। A से लाल और B से नीली होने की probability ज्ञात करें।
- A. 20/143 (Correct)
- B. 457/4290
- C. 743/4290
- D. 3/8
Explanation: Independent draws: P = 5/11 × 4/13 = 20/143. / Independent draws: P = 5/11 × 4/13 = 20/143.
- Probability — Two-bag probability
2. Bag A has 6 red balls out of 12 balls. Bag B has 5 blue balls out of 14 balls. One ball is drawn from each bag. Find probability of red from A and blue from B. / Bag A में 12 में से 6 लाल गेंदें हैं। Bag B में 14 में से 5 नीली गेंदें हैं। हर bag से एक गेंद निकली। A से लाल और B से नीली होने की probability ज्ञात करें।
- A. 5/28 (Correct)
- B. 61/420
- C. 11/26
- D. 89/420
Explanation: Independent draws: P = 6/12 × 5/14 = 5/28. / Independent draws: P = 6/12 × 5/14 = 5/28.
- Probability — Two-bag probability
3. Bag A has 7 red balls out of 13 balls. Bag B has 6 blue balls out of 15 balls. One ball is drawn from each bag. Find probability of red from A and blue from B. / Bag A में 13 में से 7 लाल गेंदें हैं। Bag B में 15 में से 6 नीली गेंदें हैं। हर bag से एक गेंद निकली। A से लाल और B से नीली होने की probability ज्ञात करें।
- A. 13/28
- B. 71/390
- C. 14/65 (Correct)
- D. 97/390
Explanation: Independent draws: P = 7/13 × 6/15 = 14/65. / Independent draws: P = 7/13 × 6/15 = 14/65.
- Probability — P&C probability
4. From 12 persons including 2 special persons, a committee of 3 is selected. Find probability that exactly one special person is selected. / 12 व्यक्तियों में 2 विशेष व्यक्ति हैं। 3 की committee चुनी जाती है। ठीक एक विशेष व्यक्ति चयनित होने की probability ज्ञात करें।
- A. 79/220
- B. 1/2
- C. 101/220
- D. 9/22 (Correct)
Explanation: Exactly one special = 2C1×10C2; total = 12C3. Probability = 9/22. / ठीक एक विशेष = 2C1×10C2; कुल = 12C3. Probability = 9/22.
- Probability — P&C probability
5. From 8 persons including 2 special persons, a committee of 3 is selected. Find probability that exactly one special person is selected. / 8 व्यक्तियों में 2 विशेष व्यक्ति हैं। 3 की committee चुनी जाती है। ठीक एक विशेष व्यक्ति चयनित होने की probability ज्ञात करें।
- A. 1/2
- B. 41/70
- C. 15/28 (Correct)
- D. 17/35
Explanation: Exactly one special = 2C1×6C2; total = 8C3. Probability = 15/28. / ठीक एक विशेष = 2C1×6C2; कुल = 8C3. Probability = 15/28.
- Probability — P&C probability
6. From 9 persons including 2 special persons, a committee of 3 is selected. Find probability that exactly one special person is selected. / 9 व्यक्तियों में 2 विशेष व्यक्ति हैं। 3 की committee चुनी जाती है। ठीक एक विशेष व्यक्ति चयनित होने की probability ज्ञात करें।
- A. 11/20
- B. 1
- C. 9/20
- D. 1/2 (Correct)
Explanation: Exactly one special = 2C1×7C2; total = 9C3. Probability = 1/2. / ठीक एक विशेष = 2C1×7C2; कुल = 9C3. Probability = 1/2.
- Probability — Complement/color selection
7. A bag has 8 red, 7 blue and 6 green balls. Two balls are drawn without replacement. Find probability that no green ball is drawn. / एक थैले में 8 लाल, 7 नीली और 6 हरी गेंदें हैं। बिना replacement दो गेंदें निकाली गईं। कोई हरी गेंद न आने की probability ज्ञात करें।
- A. 1/2 (Correct)
- B. 9/20
- C. 11/20
- D. 2/7
Explanation: No green means both from red+blue = 15. Probability = 15C2/21C2 = 1/2. / No green का अर्थ दोनों red+blue से = 15. Probability = 15C2/21C2 = 1/2.
- Probability — Complement/color selection
8. A bag has 5 red, 4 blue and 3 green balls. Two balls are drawn without replacement. Find probability that no green ball is drawn. / एक थैले में 5 लाल, 4 नीली और 3 हरी गेंदें हैं। बिना replacement दो गेंदें निकाली गईं। कोई हरी गेंद न आने की probability ज्ञात करें।
- A. 109/220
- B. 6/11 (Correct)
- C. 1/4
- D. 131/220
Explanation: No green means both from red+blue = 9. Probability = 9C2/12C2 = 6/11. / No green का अर्थ दोनों red+blue से = 9. Probability = 9C2/12C2 = 6/11.
- Probability — Conditional probability
9. A card drawn from a deck is known to be red. Find probability that it is a face card. / गड्डी से निकला पत्ता red है। उसके face card होने की probability ज्ञात करें।
- A. 3/13 (Correct)
- B. 4/13
- C. 2/13
- D. 1/2
Explanation: Given the card is red, sample space = 26 red cards. Red face cards = 6. Probability=6/26=3/13. / Card red है, इसलिए sample space = 26 red cards. Red face cards = 6. Probability=6/26=3/13.
- Probability — Conditional probability
10. A card drawn from a deck is known to be red. Find probability that it is a face card. / गड्डी से निकला पत्ता red है। उसके face card होने की probability ज्ञात करें।
- A. 3/13 (Correct)
- B. 1/2
- C. 4/13
- D. 2/13
Explanation: Given the card is red, sample space = 26 red cards. Red face cards = 6. Probability=6/26=3/13. / Card red है, इसलिए sample space = 26 red cards. Red face cards = 6. Probability=6/26=3/13.
- Probability — Two-bag probability
11. Bag A has 7 red balls out of 11 balls. Bag B has 6 blue balls out of 13 balls. One ball is drawn from each bag. Find probability of red from A and blue from B. / Bag A में 11 में से 7 लाल गेंदें हैं। Bag B में 13 में से 6 नीली गेंदें हैं। हर bag से एक गेंद निकली। A से लाल और B से नीली होने की probability ज्ञात करें।
- A. 1403/4290
- B. 42/143 (Correct)
- C. 13/24
- D. 1117/4290
Explanation: Independent draws: P = 7/11 × 6/13 = 42/143. / Independent draws: P = 7/11 × 6/13 = 42/143.
- Probability — Two-bag probability
12. Bag A has 4 red balls out of 12 balls. Bag B has 3 blue balls out of 14 balls. One ball is drawn from each bag. Find probability of red from A and blue from B. / Bag A में 12 में से 4 लाल गेंदें हैं। Bag B में 14 में से 3 नीली गेंदें हैं। हर bag से एक गेंद निकली। A से लाल और B से नीली होने की probability ज्ञात करें।
- A. 7/26
- B. 4/105
- C. 11/105
- D. 1/14 (Correct)
Explanation: Independent draws: P = 4/12 × 3/14 = 1/14. / Independent draws: P = 4/12 × 3/14 = 1/14.
- Probability — Two-bag probability
13. Bag A has 5 red balls out of 13 balls. Bag B has 4 blue balls out of 15 balls. One ball is drawn from each bag. Find probability of red from A and blue from B. / Bag A में 13 में से 5 लाल गेंदें हैं। Bag B में 15 में से 4 नीली गेंदें हैं। हर bag से एक गेंद निकली। A से लाल और B से नीली होने की probability ज्ञात करें।
- A. 9/130
- B. 4/39 (Correct)
- C. 9/28
- D. 53/390
Explanation: Independent draws: P = 5/13 × 4/15 = 4/39. / Independent draws: P = 5/13 × 4/15 = 4/39.
- Probability — P&C probability
14. From 12 persons including 2 special persons, a committee of 3 is selected. Find probability that exactly one special person is selected. / 12 व्यक्तियों में 2 विशेष व्यक्ति हैं। 3 की committee चुनी जाती है। ठीक एक विशेष व्यक्ति चयनित होने की probability ज्ञात करें।
- A. 9/22 (Correct)
- B. 1/2
- C. 101/220
- D. 79/220
Explanation: Exactly one special = 2C1×10C2; total = 12C3. Probability = 9/22. / ठीक एक विशेष = 2C1×10C2; कुल = 12C3. Probability = 9/22.
- Probability — P&C probability
15. From 8 persons including 2 special persons, a committee of 3 is selected. Find probability that exactly one special person is selected. / 8 व्यक्तियों में 2 विशेष व्यक्ति हैं। 3 की committee चुनी जाती है। ठीक एक विशेष व्यक्ति चयनित होने की probability ज्ञात करें।
- A. 41/70
- B. 1/2
- C. 17/35
- D. 15/28 (Correct)
Explanation: Exactly one special = 2C1×6C2; total = 8C3. Probability = 15/28. / ठीक एक विशेष = 2C1×6C2; कुल = 8C3. Probability = 15/28.
- Probability — P&C probability
16. From 9 persons including 2 special persons, a committee of 3 is selected. Find probability that exactly one special person is selected. / 9 व्यक्तियों में 2 विशेष व्यक्ति हैं। 3 की committee चुनी जाती है। ठीक एक विशेष व्यक्ति चयनित होने की probability ज्ञात करें।
- A. 1/2 (Correct)
- B. 11/20
- C. 1
- D. 9/20
Explanation: Exactly one special = 2C1×7C2; total = 9C3. Probability = 1/2. / ठीक एक विशेष = 2C1×7C2; कुल = 9C3. Probability = 1/2.
- Probability — Complement/color selection
17. A bag has 6 red, 5 blue and 4 green balls. Two balls are drawn without replacement. Find probability that no green ball is drawn. / एक थैले में 6 लाल, 5 नीली और 4 हरी गेंदें हैं। बिना replacement दो गेंदें निकाली गईं। कोई हरी गेंद न आने की probability ज्ञात करें।
- A. 199/420
- B. 4/15
- C. 241/420
- D. 11/21 (Correct)
Explanation: No green means both from red+blue = 11. Probability = 11C2/15C2 = 11/21. / No green का अर्थ दोनों red+blue से = 11. Probability = 11C2/15C2 = 11/21.
- Probability — Complement/color selection
18. A bag has 7 red, 6 blue and 5 green balls. Two balls are drawn without replacement. Find probability that no green ball is drawn. / एक थैले में 7 लाल, 6 नीली और 5 हरी गेंदें हैं। बिना replacement दो गेंदें निकाली गईं। कोई हरी गेंद न आने की probability ज्ञात करें।
- A. 26/51 (Correct)
- B. 571/1020
- C. 469/1020
- D. 5/18
Explanation: No green means both from red+blue = 13. Probability = 13C2/18C2 = 26/51. / No green का अर्थ दोनों red+blue से = 13. Probability = 13C2/18C2 = 26/51.
- Probability — Conditional probability
19. A card drawn from a deck is known to be red. Find probability that it is a face card. / गड्डी से निकला पत्ता red है। उसके face card होने की probability ज्ञात करें।
- A. 4/13
- B. 1/2
- C. 3/13 (Correct)
- D. 2/13
Explanation: Given the card is red, sample space = 26 red cards. Red face cards = 6. Probability=6/26=3/13. / Card red है, इसलिए sample space = 26 red cards. Red face cards = 6. Probability=6/26=3/13.
- Probability — Conditional probability
20. A card drawn from a deck is known to be red. Find probability that it is a face card. / गड्डी से निकला पत्ता red है। उसके face card होने की probability ज्ञात करें।
- A. 1/2
- B. 3/13 (Correct)
- C. 4/13
- D. 2/13
Explanation: Given the card is red, sample space = 26 red cards. Red face cards = 6. Probability=6/26=3/13. / Card red है, इसलिए sample space = 26 red cards. Red face cards = 6. Probability=6/26=3/13.
- Probability — Percentage / प्रतिशत
21. 25% of 600 is: / 600 का 25% कितना है?
- A. 140
- B. 150 (Correct)
- C. 160
- D. 170
Explanation: 25% = 25/100, so answer = 150. / प्रतिशत को 100 से भाग देकर मूल संख्या से गुणा करें।
- Probability — Profit-Loss / लाभ-हानि
22. An article bought for Rs 850 is sold at 12.5% profit. Find SP. / Rs 850 में खरीदी वस्तु 12.5% लाभ पर बेची गई। SP ज्ञात करें।
- A. Rs 916
- B. Rs 956 (Correct)
- C. Rs 996
- D. Rs 1036
Explanation: SP = CP x (100 + profit%)/100 = 850 x 112.5/100 = Rs 956. / लाभ प्रतिशत जोड़कर विक्रय मूल्य निकालें।
- Probability — Time & Work / समय और कार्य
23. A finishes a work in 15 days and B in 21 days. Together they finish in: / A 15 दिन और B 21 दिन में काम पूरा करते हैं। साथ में समय?
- A. 7.800000000000001 days
- B. 8.8 days (Correct)
- C. 9.8 days
- D. 10.8 days
Explanation: Combined time = ab/(a+b) = 15 x 21 / 36 = 8.8 days. / संयुक्त कार्य में दरें जोड़ी जाती हैं।
- Probability — Speed Conversion / चाल परिवर्तन
24. 108 km/h equals: / 108 किमी/घंटा बराबर है:
- A. 27 m/s
- B. 30 m/s (Correct)
- C. 33 m/s
- D. 35 m/s
Explanation: km/h to m/s conversion uses x 5/18. 108 x 5/18 = 30. / किमी/घंटा को मी/से में बदलने के लिए 5/18 से गुणा करें।
- Probability — Simplification / सरलीकरण
25. Simplify: 25 x 18 + 25 - 18. / सरल करें: 25 x 18 + 25 - 18.
- A. 449
- B. 457 (Correct)
- C. 465
- D. 473
Explanation: Apply BODMAS: 450 + 25 - 18 = 457. / पहले गुणा, फिर जोड़-घटाव करें।