# JAC 12th Mathematics Important Questions Ch 13 Probability

JAC 12th Mathematics Important Questions Ch 13 2023: झारखण्ड बोर्ड कक्षा 12th सभी विद्यार्थियों के लिए Maths में chapter 13 Probability के पिछले वर्षो में जो भी प्रश्न पूछे गए हैं, उनकी चर्चा हम इसमें करेंगे तो इन Important Questions को पढ़ लीजिए.

रांची: झारखंड एकेडमिक काउंसिल ( JAC Board) कक्षा JAC 12th Maths Important Questions के पिछले वर्षों के सभी महत्वपूर्ण प्रश्न (important Questions) आपको यहाँ पर बताए जा रहे है, जो बोर्ड परीक्षा 2023 के लिए बहुत महत्वपूर्ण है. अगर आप इन सभी प्रश्नों को याद कर लेते हो तो अवश्य ही आप JAC Board class 12th Maths  exam 2023 में अच्छे अंक प्राप्त कर सकते हो.

यदि आप ऐसे ही सभी विषयों के Chapterwise Important Questions उत्तर चाहते हैं तो हमारे वेबसाइट jharkhandlab.com से जुड़े रहे.

विद्यार्थी इसका उत्तर स्वयं करें। ये सारे प्रश्न आपके परीक्षा (JAC 12th Maths Important Questions For Board Exams)में बार – बार पूछे जा रहे है। इसमें आपको सभी chapter का अलग-अलग पिछले 16 से 17 वर्षों के महत्वपूर्ण प्रश्न मिलेंगे। यानि 2006-2022 इसमें आपको ये भी बताया जा रहा है कि कौन से प्रश्न किस तरह से एवं कितने marks के पूछे जा रहें है.

यदि वैसे छात्र छात्राएं जो प्रश्नों के उत्तर नहीं कर पाते हैं, वो कुछ दिन प्रतीक्षा करें. आप यहाँ से Questions-answers download कर सकते हैं.

## JAC 12th Mathematics Important Questions Ch 13-Overview

### परीक्षा की तैयारी कैसे करें?

परीक्षा की बेहतरीन तैयारी करने के लिए कुछ महत्वपूर्ण बातें को ध्यान में रख कर पढ़ाई करें , ये बातें कुछ इस प्रकार हैं –

• Study Schedule बनाएं: एक Study schedule बनाए ताकि आप जेएसी(JAC Board) 12वीं रूटीन 2023 की सहायता से पहले ही पूरा syllabus कवर कर सके, परीक्षा से पहले syllabus को पूरा करने से revision के लिए पर्याप्त समय मिलेगा.
• Short Notes बनाएं: विषयोंको important points में सारांशित करके छोटे notes बनाने से Revision भाग को आसान बनाने में मदद मिलेगी, इसके अलावा छात्र विषयों का रिवीजन करने के लिए हर जगह भारी पाठ्य Books ले जाने से बच सकते हैं.
• परीक्षा से पहले पूरा करें Syllabus : 12वीं के syllabus का पता होना छात्रों के लिए important है क्योंकि इससे महत्वपूर्ण विषयों, परीक्षा की अवधि और अंकन योजना के बारे में जानकारी मिलती है. छात्रों को सलाह दी गई है कि वे 12वीं Routine 2023 जारी होने से पहले पाठ्यक्रम को पूरा कर ले।
• पिछले साल के प्रश्नपत्रों को हल करें:पिछले साल के 12वीं के प्रश्न पत्री का अभ्यास करना परीक्षा को सफलतापूर्वक पास करने की कुंजी है, तैयारी के स्तर का आत्म विश्लेषण करने के लिए छात्रों को सभी subjects के प्रश्न पत्रों का revision करना चाहिए, इसके अलावा यह students को समय प्रबंधन सीखने और गणना की गति में सुधार करने में भी help कर सकता है.

### JAC 12th Mathematics Previous Years Important Questions-

Q1. Three unbiased coins are tossed simultaneously. What is the probability of getting atleast one head? (2006)
Q2. A doctor claims that every three out of five persons he examines are allergic to some type of weed. What is the probability that exactly three out of the next four patients are allergic to weeds? (2006)
Q3. A speaks truth in 75% cases and B in 80% of the cases. In what percent are they likely to contradict each other in narrating the same statement? (2007)

Q4. If P(A)=2/5, P(B)= 1/3 and P(AUB)= 1/2, then find P(A/B) and P(B/A). (2007)
Q5. If P(A)=0.6, P(B) = 0.3 and P(A∩B) = 0.1, find P(A’∩B’). 
Q6. A and B appear for an interview. Probability of A’s success is 3/4 and that of B’s success is1/5. What is the probability that only one of them is selected.
Q7. A coin is tossed 12 times. What is the probability that exactly 10 heads appear? 

Q8. A bag A contains 3 white and 2 red balls and another bag B contains 5 white and 4 real balls. One ball is drawn at random from one of them bags and it is found to be red. What is the probability that it was drawn from the bag B? (2009)
Q9. Two coins are thrown simultaneously. Find the Probability of the event when head will appear on both of them. (2010)
Q10. If a coin is tossed n times. What is the probability that head appears an odd number of times. (2010)
Q11. A man throws two dices. What is the probability of getting exactly 4 aces on both in 6 trails ? (2010)

Q12. A bag contains 3 white and 2 black balls find the probability of drawing a white  ball at random. (2011, 2013)
Q13. What is the chance of getting 7 or 11 in with 2 dice? (2011)
Q14. Find the odds in favour and odds against drawing 2 Kings from a pack of 52 cards. (2011)
Q15. If P(B)=0.5 and P(A∩B)=0.32 then the value of P(A/B) is – (2012)
A.15/22
B. 16/25
C. 14/25
D. 13/25
Q16. 10 coins are tossed. What is the probability that exactly 5 heads appear?  (2012, 2013)

Q17. A card is drawn from an ordinary pack and a gambler bets that it is a spade or an ace. What are the odds against his winning the bet?(2012)
Q18. A coin is tossed 3 times. Find the probability that exactly 2 heads. (2013)
Q19. If A and B are two independent events such that P(A)=0.35 and P(AUB)=0.6, find P(B). (2014)

Q20. A manufacturer has three machine operators A, B and C. The first operator A produces 1% defetive items, whereas the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B on the job for 30% of the time and C on the job for 20% of the time. Let E1 : be event that an item is produced by A, E2: be event that an item is produced by B and E3 : be event that an item produced by C. If E be the event that a defective item is produced, then find the following: (2014)
i. P(E1)
ii. P(E2)
iii.P(E3)
iv. P(E/E1)
v. P(E/E2)
vi. P(E/E3)

Q21. Let A and B be two events such that 2P(A) = P(B)=5/13 and P(A/B)=2/5. Find P(AB). (2015)

Q22. Urn A contains 1 white, 2 black and 3 red balls. Urn B contains 2 white 1 black and 1 red balls and Urn C contains 4 white, 5 black and 3 red balls. One urn is selected at random and two balls are drawn. Let E be the event that the balls drawn are one white and one red and E1, E2, E3, be events that selected urns are A, B and C respectively. Now find the following: (2015)
(i) P(E₁)
(ii) P(E₂)
(iii) P(E/E3)
(iv) P (E/E₁)
Q23. A family has two children. What is the probability that both the children are boys, given that at least one of them is a boy? (2016)

Q24. It is known about a person that he speaks the truth 3 times out of 5. Let E be the event that the person throws a die and declares that the number on the die is 4. Also let A, B be events that the number on the die is 4 and other than 4 respectively. Now find the following: (2016)
(ii) P(B)
(i) P(A)
(iv) P (E/B)
(v) P(A/E)
(iii) P(E/A)
(vi) P (B/E)

Q25. If a coin is tossed three times,  find P(E/F), where
E→ at least two heads ;
F→ at most two heads. (2017)

Q26. A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamond. Find the probability of the lost card being a diamond. [JAC-2019]
Q27. Let A and B be event such that P(A)=7/18, P(B)=9/13 and P(A∩B)=4/13. Find – (2018)
i. P(A/B)
ii. P(B/A)
iii. P(A∪B)
iv. P(B’/A’)

Q28. Two dice thrown. Find the Probability that the numbers appeared has a sum 8, if it is known that the second dice is always exhibit 4.(2018)
Q29. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident involving a scooter, a car and a truck are 0.01, 0.03 and 0.15 respectively. One of the insured drivers meets with an accident. What is the probability that he is a scooter driver.(2018)

Q30. Six coins are tossed simultaneously. Find the probability of getting- (2018)
(iii) not more than 3 heads
Q31. Two cards are drawn at random and without replacement from a pack of 52 cards. Find the probability that both are black. (2019)
Q32. If 2P(A) = P(B) =5/13 and P(A/B)=2/5, then find P(AB).

Q33. A person buys 50 tickets of a lottery, in each of which his chance of winning a prize is 1/100. What is the probability that he will win a prize (a) at least once, (b) exactly once, (c) at least twice? (2019)
Q34. Mother, father and son line up at random for a family picture. Find P(E/F). where ,
E→ Son on one end
F → Father in middle (2020)

Q35. Bag A contains 2 red and 3 black balls white another Bag B contains 3 red and 4 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag B. (2020)
Q36. Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Find the probability distribution of the number of aces.(2020)

Q37. If P(A)=7/13, P(B)=9/13 and P(A∩B)=4/13 then find P(A/B).
Q38. If P(A)=0.8, P(B)=0.5 , P(B/A)=0.4 , then find (2022)
i. P(AB) ii. P(A∩B) iii.P(A/B)

### Previous years papers से कितने Questions पूछे जायेंगे?

अधिक से अधिक Questions Previous years papers से ही पूछे जायेंगे।

### यह Previous years का पेपर कब से कब तक का है?

यह Previous years का पेपर 2006 से 2022 तक का है।

### Model पेपर कब तक आएगा?

मॉडल पेपर अगले महीने यानि 15 january से पहले आ जाएगा।

### Model पेपर से कितने Questions पूछे जायेंगे?

2022 में 80% प्रश्न मॉडल सेट के अंदर से ही पूछे गए थें, तो इस बार भी ऐसे ही पूछे जाएँगे। Hey, I’m Vikash Kumar, I’m the owner of this website from Jharkhand. I’m still studying, in this website, you will see many categories of blogs. if you want to contact me then contact via vikashkrprasad23@gmail.com