Probability Test 7

Bilingual timed test for SSC, RRB and Banking quant with clean Hindi, preserved math symbols and detailed solutions.

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Batch 2 | SSC RRB Banking

Probability Test 7

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.

Questions

Duration

25 min

Marking

+1 / -0.25

Sections

Probability | 25 questions

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Preview all 25 questions in Probability Test 7 (no login required)

Probability — Without replacement
1. A bag contains 5 red and 6 blue balls. Two balls are drawn without replacement. Find probability both are red. / थैले में 5 लाल और 6 नीली गेंदें हैं। बिना replacement दो गेंदें निकाली गईं। दोनों लाल होने की probability ज्ञात करें।
- A. 29/220
- B. 51/220
- C. 5/11
- D. 2/11 (Correct)
Explanation: Without replacement: P(two red) = 5/11 × 4/10 = 2/11. / बिना replacement: P(दोनों लाल) = 5/11 × 4/10 = 2/11.
Probability — Without replacement
2. A bag contains 6 red and 7 blue balls. Two balls are drawn without replacement. Find probability both are red. / थैले में 6 लाल और 7 नीली गेंदें हैं। बिना replacement दो गेंदें निकाली गईं। दोनों लाल होने की probability ज्ञात करें।
- A. 6/13
- B. 5/26 (Correct)
- C. 63/260
- D. 37/260
Explanation: Without replacement: P(two red) = 6/13 × 5/12 = 5/26. / बिना replacement: P(दोनों लाल) = 6/13 × 5/12 = 5/26.
Probability — Card combination probability
3. Two cards are drawn from a deck of 52 cards. Find probability that both are aces. / 52 पत्तों की गड्डी से दो पत्ते निकाले गए। दोनों ace होने की probability ज्ञात करें।
- A. 2/221
- B. 1/221 (Correct)
- C. 3/221
- D. 1/13
Explanation: Two aces from 4 aces in 52 cards: probability = 4C2/52C2 = 1/221. / 52 पत्तों में 4 aces हैं। Probability = 4C2/52C2 = 1/221.
Probability — Card combination probability
4. Two cards are drawn from a deck of 52 cards. Find probability that both are aces. / 52 पत्तों की गड्डी से दो पत्ते निकाले गए। दोनों ace होने की probability ज्ञात करें।
- A. 1/13
- B. 2/221
- C. 3/221
- D. 1/221 (Correct)
Explanation: Two aces from 4 aces in 52 cards: probability = 4C2/52C2 = 1/221. / 52 पत्तों में 4 aces हैं। Probability = 4C2/52C2 = 1/221.
Probability — Exactly one event
5. Two coins are tossed. Find probability of getting exactly one head. / दो सिक्के उछाले गए। ठीक एक head आने की probability ज्ञात करें।
- A. 1/8
- B. 1/2 (Correct)
- C. 3/4
- D. 1/4
Explanation: Outcomes: HH, HT, TH, TT. Exactly one head: HT, TH = 2 outcomes. Probability=2/4=1/2. / परिणाम: HH, HT, TH, TT. ठीक एक head: HT, TH = 2 परिणाम। Probability=2/4=1/2.
Probability — Exactly one event
6. Two coins are tossed. Find probability of getting exactly one head. / दो सिक्के उछाले गए। ठीक एक head आने की probability ज्ञात करें।
- A. 3/4
- B. 1/4
- C. 1/2 (Correct)
- D. 1/8
Explanation: Outcomes: HH, HT, TH, TT. Exactly one head: HT, TH = 2 outcomes. Probability=2/4=1/2. / परिणाम: HH, HT, TH, TT. ठीक एक head: HT, TH = 2 परिणाम। Probability=2/4=1/2.
Probability — Complement probability
7. A lot has 17 items including 3 defective items. Two are selected. Find probability that at least one is defective. / एक lot में 17 वस्तुएँ हैं जिनमें 3 defective हैं। दो चुनी जाती हैं। कम से कम एक defective होने की probability ज्ञात करें।
- A. 45/136 (Correct)
- B. 3/17
- C. 259/680
- D. 191/680
Explanation: P(at least one defective) = 1 − P(no defective) = 1 − 14C2/17C2 = 45/136. / P(कम से कम एक defective) = 1 − P(कोई defective नहीं) = 1 − 14C2/17C2 = 45/136.
Probability — Complement probability
8. A lot has 10 items including 4 defective items. Two are selected. Find probability that at least one is defective. / एक lot में 10 वस्तुएँ हैं जिनमें 4 defective हैं। दो चुनी जाती हैं। कम से कम एक defective होने की probability ज्ञात करें।
- A. 2/3 (Correct)
- B. 43/60
- C. 37/60
- D. 2/5
Explanation: P(at least one defective) = 1 − P(no defective) = 1 − 6C2/10C2 = 2/3. / P(कम से कम एक defective) = 1 − P(कोई defective नहीं) = 1 − 6C2/10C2 = 2/3.
Probability — Two dice sum
9. Two dice are thrown. Find probability that the sum is 7. / दो पासे फेंके गए। योग 7 आने की probability ज्ञात करें।
- A. 1/6 (Correct)
- B. 1/9
- C. 1/4
- D. 1/12
Explanation: Sum 7 outcomes: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6. Probability=6/36=1/6. / योग 7 के परिणाम: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)=6. Probability=6/36=1/6.
Probability — Two dice sum
10. Two dice are thrown. Find probability that the sum is 7. / दो पासे फेंके गए। योग 7 आने की probability ज्ञात करें।
- A. 1/12
- B. 1/9
- C. 1/6 (Correct)
- D. 1/4
Explanation: Sum 7 outcomes: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6. Probability=6/36=1/6. / योग 7 के परिणाम: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)=6. Probability=6/36=1/6.
Probability — Without replacement
11. A bag contains 5 red and 6 blue balls. Two balls are drawn without replacement. Find probability both are red. / थैले में 5 लाल और 6 नीली गेंदें हैं। बिना replacement दो गेंदें निकाली गईं। दोनों लाल होने की probability ज्ञात करें।
- A. 51/220
- B. 2/11 (Correct)
- C. 29/220
- D. 5/11
Explanation: Without replacement: P(two red) = 5/11 × 4/10 = 2/11. / बिना replacement: P(दोनों लाल) = 5/11 × 4/10 = 2/11.
Probability — Without replacement
12. A bag contains 6 red and 7 blue balls. Two balls are drawn without replacement. Find probability both are red. / थैले में 6 लाल और 7 नीली गेंदें हैं। बिना replacement दो गेंदें निकाली गईं। दोनों लाल होने की probability ज्ञात करें।
- A. 37/260
- B. 5/26 (Correct)
- C. 6/13
- D. 63/260
Explanation: Without replacement: P(two red) = 6/13 × 5/12 = 5/26. / बिना replacement: P(दोनों लाल) = 6/13 × 5/12 = 5/26.
Probability — Card combination probability
13. Two cards are drawn from a deck of 52 cards. Find probability that both are aces. / 52 पत्तों की गड्डी से दो पत्ते निकाले गए। दोनों ace होने की probability ज्ञात करें।
- A. 2/221
- B. 1/221 (Correct)
- C. 1/13
- D. 3/221
Explanation: Two aces from 4 aces in 52 cards: probability = 4C2/52C2 = 1/221. / 52 पत्तों में 4 aces हैं। Probability = 4C2/52C2 = 1/221.
Probability — Card combination probability
14. Two cards are drawn from a deck of 52 cards. Find probability that both are aces. / 52 पत्तों की गड्डी से दो पत्ते निकाले गए। दोनों ace होने की probability ज्ञात करें।
- A. 1/13
- B. 1/221 (Correct)
- C. 3/221
- D. 2/221
Explanation: Two aces from 4 aces in 52 cards: probability = 4C2/52C2 = 1/221. / 52 पत्तों में 4 aces हैं। Probability = 4C2/52C2 = 1/221.
Probability — Exactly one event
15. Two coins are tossed. Find probability of getting exactly one head. / दो सिक्के उछाले गए। ठीक एक head आने की probability ज्ञात करें।
- A. 1/4
- B. 3/4
- C. 1/8
- D. 1/2 (Correct)
Explanation: Outcomes: HH, HT, TH, TT. Exactly one head: HT, TH = 2 outcomes. Probability=2/4=1/2. / परिणाम: HH, HT, TH, TT. ठीक एक head: HT, TH = 2 परिणाम। Probability=2/4=1/2.
Probability — Exactly one event
16. Two coins are tossed. Find probability of getting exactly one head. / दो सिक्के उछाले गए। ठीक एक head आने की probability ज्ञात करें।
- A. 1/8
- B. 1/4
- C. 3/4
- D. 1/2 (Correct)
Explanation: Outcomes: HH, HT, TH, TT. Exactly one head: HT, TH = 2 outcomes. Probability=2/4=1/2. / परिणाम: HH, HT, TH, TT. ठीक एक head: HT, TH = 2 परिणाम। Probability=2/4=1/2.
Probability — Complement probability
17. A lot has 11 items including 4 defective items. Two are selected. Find probability that at least one is defective. / एक lot में 11 वस्तुएँ हैं जिनमें 4 defective हैं। दो चुनी जाती हैं। कम से कम एक defective होने की probability ज्ञात करें।
- A. 147/220
- B. 4/11
- C. 25/44
- D. 34/55 (Correct)
Explanation: P(at least one defective) = 1 − P(no defective) = 1 − 7C2/11C2 = 34/55. / P(कम से कम एक defective) = 1 − P(कोई defective नहीं) = 1 − 7C2/11C2 = 34/55.
Probability — Complement probability
18. A lot has 12 items including 2 defective items. Two are selected. Find probability that at least one is defective. / एक lot में 12 वस्तुएँ हैं जिनमें 2 defective हैं। दो चुनी जाती हैं। कम से कम एक defective होने की probability ज्ञात करें।
- A. 59/220
- B. 7/22 (Correct)
- C. 81/220
- D. 1/6
Explanation: P(at least one defective) = 1 − P(no defective) = 1 − 10C2/12C2 = 7/22. / P(कम से कम एक defective) = 1 − P(कोई defective नहीं) = 1 − 10C2/12C2 = 7/22.
Probability — Two dice sum
19. Two dice are thrown. Find probability that the sum is 7. / दो पासे फेंके गए। योग 7 आने की probability ज्ञात करें।
- A. 1/9
- B. 1/6 (Correct)
- C. 1/4
- D. 1/12
Explanation: Sum 7 outcomes: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6. Probability=6/36=1/6. / योग 7 के परिणाम: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)=6. Probability=6/36=1/6.
Probability — Two dice sum
20. Two dice are thrown. Find probability that the sum is 7. / दो पासे फेंके गए। योग 7 आने की probability ज्ञात करें।
- A. 1/12
- B. 1/6 (Correct)
- C. 1/4
- D. 1/9
Explanation: Sum 7 outcomes: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6. Probability=6/36=1/6. / योग 7 के परिणाम: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)=6. Probability=6/36=1/6.
Probability — Percentage / प्रतिशत
21. 25% of 400 is: / 400 का 25% कितना है?
- A. 90
- B. 100 (Correct)
- C. 110
- D. 120
Explanation: 25% = 25/100, so answer = 100. / प्रतिशत को 100 से भाग देकर मूल संख्या से गुणा करें।
Probability — Profit-Loss / लाभ-हानि
22. An article bought for Rs 1150 is sold at 20% profit. Find SP. / Rs 1150 में खरीदी वस्तु 20% लाभ पर बेची गई। SP ज्ञात करें।
- A. Rs 1340
- B. Rs 1380 (Correct)
- C. Rs 1420
- D. Rs 1460
Explanation: SP = CP x (100 + profit%)/100 = 1150 x 120/100 = Rs 1380. / 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. 72 km/h equals: / 72 किमी/घंटा बराबर है:
- A. 17 m/s
- B. 20 m/s (Correct)
- C. 23 m/s
- D. 25 m/s
Explanation: km/h to m/s conversion uses x 5/18. 72 x 5/18 = 20. / किमी/घंटा को मी/से में बदलने के लिए 5/18 से गुणा करें।
Probability — Simplification / सरलीकरण
25. Simplify: 26 x 16 + 26 - 16. / सरल करें: 26 x 16 + 26 - 16.
- A. 418
- B. 426 (Correct)
- C. 434
- D. 442
Explanation: Apply BODMAS: 416 + 26 - 16 = 426. / पहले गुणा, फिर जोड़-घटाव करें।