BAYE'S THEOREM | L-7 | PROBABILITY | CLASS-12 | NCERT-MATHS

THIS VIDEO LECTURE INCLUDES
1. DETAILED EXPLANATION WITH PROOF OF TOTAL PROBABILITY THEOREM AND BAYE'S THEOREM
2. DETAILED SOLUTION OF NCERT CLASS12 MATHS NCERT PROBABILITY SOLVED EXAMPLES 15-21
3.A PERSON HAS UNDERTAKEN A CONSTRUCTION JOB. PROBABILITIES ARE 0.65 THAT THERE WILL BE STRIKE,0.80 THAT THE CONSTRUCTION JOB WILL BE COMPLETED ON TIME IF THERE IS NO STRIKE AND 0.32 THAT THE CONSTRUCTION JOB WILL BE COMPLETED ON TIME IF THERE IS A STRIKE. DETERMINE THE PROBABILITY THAT THE CONSTRUCTION JOB WILL BE COMPLETED ON TIME
4. BAG I CONTAINS 3 RED AND 4 BLACK BALLS WHILE ANOTHER BAG II CONTAINS 5 RED AND 6 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 II.
5. GIVEN THREE IDENTICAL BOXES I,II AND III EACH CONTAINING TWO COINS. IN BOX I BOTH COINS ARE GOLD COINS , IN BOX II BOTH ARE SILVER COINS AND IN BOX III THERE IS ONE GOLD AND ONE SILVER COINS. A PERSON CHOOSES A BOX AT RANDOM AND TAKES OUT A COIN. IF THE COIN IS OF GOLD, WHAT IS THE PROBABILITY THAT THE OTHER COIN IN THE BOX IS ALSO OF GOLD?
6. SUPPOSE THAT THE RELIABILITY OF A HIV TEST IS SPECIFIED AS FOLLOWS:
OF PEOPLE HAVING HIV, 90% OF THE TEST DETECT THE DISEASE BUT 10% GO UNDETECTED. OF PEOPLE FREE OF HIV 99% OF THE TEST ARE JUDGED HIV -IVE BUT 1% ARE DIAGNOSED AS SHOWING HIV +IVE. FROM A LARGE POPULATION OF WHICH ONLY 0.1% HAVE HIV , ONE PERSON IS SELECTED AT RANDOM GIVEN THE HIV TEST, AND THE PATHOLOGIST REPORTS HIM/HER AS HIV +IVE. WHAT IS THE PROBABILITY THAT THE PERSON ACTUALLY HAS HIV?
7.IN A FACTORY WHICH MANUFACTURES BOLTS, MACHINES A,B, AND C MANUFACTURE RESPECTIVELY 25% ,35% AND 40% OF THE BOLTS, OF THEIR BOLTS 5,4,2 PERCENT ARE RESPECTIVELY DEFECTIVE BOLTS. A BOLT IS DRAWN AT RANDOM FROM THE PRODUCT AND IS FOUND TO BE DEFECTIVE. WHAT IS THE PROBABILITIY THAT IT IS MANUFACTURE BY THE MACHINE B?
8.A DOCTOR IS TO VISIT A PATIENT. FROM THE PAST EXPERIENCE IT IS KNOWN THAT THE PROBABILITIES NOTHING WILL COME BY TRAIN BUS SCOOTER OR BY OTHER MEANS OF TRANSPORT ARE RESPECTIVELY 3/10,1/5,1/10 AND 2/5. THE PROBABILITIES THAT HE WILL BE LATE ARE 1/4,1/3,1/12 IF HE COMES BY TRAIN BUS AND SCOOTER RESPECTIVELY, BUT IF HE COMES BY OTHER MEANS OF TRANSPORT THEN HE WILL NOT BE LATE. WHEN HE ARRIVES HE IS LATE. WHAT IS THE PROBABILITY THAT HE COMES BY TRAIN?
9. MAN IS KNOWN TO SPEAK TRUTH 3 OUT OF 4 TIMES. HE THROWS A DIE AND REPORTS THAT IT IS A SIX. FIND THE PROBABILITY THAT IT IS ACTUALLY A 6?

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