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RD Sharma Class 12 Exercise 30.6 Probability Solutions Maths - Download PDF Free Online

RD Sharma Class 12 Exercise 30.6 Probability Solutions Maths - Download PDF Free Online

Edited By Kuldeep Maurya | Updated on Jan 25, 2022 04:02 PM IST

RD Sharma class 12th exercise 30.6 solution is a pretty popular choice for NCERT solutions as deduced from student reviews. We all know that the CBSE syllabus requires a thorough understanding of the NCERT book and the questions given in the book so that they can understand the concepts clearly. Mathematics is a challenging subject that needs to be practised regularly for perfection. The RD Sharma class 12 chapter 30 exercise 30.6 will help the students to master mathematics and ace their exams. It will be the perfect book for last-minute revisions.

This Story also Contains
  1. RD Sharma Class 12 Solutions Chapter30 Probability - Other Exercise
  2. Probability Excercise:30.6
  3. RD Sharma Chapter-wise Solutions

Also Read - RD Sharma Solutions For Class 9 to 12 Maths

RD Sharma Class 12 Solutions Chapter30 Probability - Other Exercise

Probability Excercise:30.6

Probability exercise 30.6 question 1

Answer:
3988
Hint:
We use the probability formula
Given:
A bag A contains 5 white and 6 black balls. Another bag B contains 4 white and 3 black balls.
Solution:
Let
E1=A white ball is transferred bag A to bag B,then drawing the black ball
E2=A black ball is transferred bag A to bag B,then drawing the black ball
A = Ball draw is back
 Probability of an event = No. of outcomes  Total outcomes P(E1)=511;P(E2)=611P(AE1)=38;P(AE2)=48
Using total probability theorem
 required probability =P(A)=P(E1)×P(AE1)+P(E2)×P(AE2)P(A)=511×38+611×48=1588+2488=15+2488=3988


Probability exercise 30.6 question 2

Answer:
1942
Hint:
We use the probability formula
Given:
Purse 1 = 2 silver ; 4 copper coins
Purse 2 = 4 silver ; 3 copper coins
Solution:
Let E1 be the event of selecting purse 1 and then drawing a silver coin from it
Let E2 be the event of selecting purse 2 and then drawing a silver coin from it
Let S be the event of drawing a silver coin
P(E1)=12;P(E2)=12P(SE1)=26;P(SE2)=47
Using total probability theorem
 required probability =P(E1)×P(SE1)+P(E2)×P(SE2)=12×26+12×47=12[26+47]=12[13+47]=12[7+1221]=1942

Probability exercise 30.6 question 3

Answer:
2945
Hint:
To solve this problem, we use
 total probability =P(E1)×P(AE1)+P(E2)×P(AE2)
Given:
One bag contains 4 yellow and 5 red balls. Another bag contains 6 yellow and 3 red balls.
Solution:
E1 = red bag from 1 to 2
E2 = yellow bag from 1 to 2
A = ball is yellow
P(E1)=59;P(E2)=49
Total balls in 2nd bag = 10
P(AE1)=610;P(AE2)=710
Using total probability theorem
 required probability =P(A)=P(E1)×P(AE1)+P(E2)×P(AE2)=59×610+49×710=13+1445=15+1445=2945

Probability exercise 30.6 question 4

Answer:
715
Hint:
To solve this we use only white balls and then total probability formula
Given:
A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls.
Solution:
Bag 1 → 3W + 2B = 5 Bag 2 → 2W + 4B = 6
P( Choosing a bag )=12P( Bag 1 )=P( Bag 2 )=12 Bag 1 = White ball P(W1)= Number of white balls  Total Number of balls =35 Bag 2 = White ball P(W1)= Number of white balls  Total Number of balls =26=13P(W)=12×35=310 probability of drawing white ball from Bag 1 P(W)=12×13=16 probability of drawing white ball from Bag 2  Total probability =310+16=9+530=1430=715


Probability exercise 30.6 question 5
Answer:
118495
Hint:
To solve this we use total probability formula.
Given:
Bag I: 1 White,2 black and 3 red balls
Bag II: 2 White,1 black and 1 red balls
Bag III: 4 White,5 black and 3 red balls
Solution:
E1=Selecting Bag 1
E2=Selecting Bag 2
E3=Selecting Bag 3
A = Drawing a white and a red ball
As one of the bag is selected randomly,
P(E1)=P(E2)=P(E3)=13P(AE1)=C1×3C16C2=315P(AE2)=2C1×1C14C2=26P(AE3)=4C1×3C112C2=1266
Using total probability theorem
 Required probability =P(E1)×P(AE1)+P(E2)×P(AE2)+P(E3)×P(AE3)=13×315+13×26+13×1266=115+19+233=33+55+30495=118495


Probability exercise 30.6 question 6

Answer:
193792
Hint:
To solve this first we find P(7 or 8) by head then P(7 & 8) by tails then required probability.
Given:
One coin – Head or Tail
Dice and 11 cards
Solution:
 Probability of an Head or Tail =(12)
Sample space of sum of the numbers of an unbiased dice when there will be head
 Sample space ={1+1;2+16+11+2;2+26+21+3;2+36+11+6;2+66+6n(S)=36
favourable outcome = 7 or 8 (Sum)
n favour = 11
P(7 or 8)=1136
Sample space of eleven cards when there will be tail,
Sample space = {2,3,4,5,6,7,8,9,10,11}
n(S)=11
favourable outcome = {7,8}, n favour = 2
P(7 or 8)=211P( 7 or 8 after getting head )=12×1136=1172 Required prob (7 or 8) =1172+111=121+7272×11=193792


Probability exercise 30.6 question 7

Answer:
0.016
Hint:
To solve this we use the total probability formula.
Given:
A=production 60%, 2% defective
B=production 40%, 1% defective
Solution:
A=60=610×2100 (that item is defective and coming from machine A )B=40=410×1100 (that item is defective and coming from machine B )
Using total probability theorem
 Required probability =610×2100+410×1100=12+41000=161000=0.016


Probability exercise 30.6 question 8

Answer:
83150
Hint:
To solve this we use total probability formula.
Given:
Bag A contains 8 white and 7 black balls & Bag B contains 5 white and 4 black balls
Solution:
E1 = Black ball transfer from Bag A to Bag B
E2 = White ball transfer from Bag A to Bag B
A = White ball drawn
P(E1)=715;P(E2)=815P(AE1)=510;P(AE2)=35
Using total probability theorem
 required probability =P(E1)×P(AE1)+P(E2)×P(AE2)=715×510+815×35=730+825=83150

Probability exercise 30.6 question 9

Answer:
3172
Hint:
To solve this we find probability of white ball
Given:
Bag I contains 4 white and 5 black balls & Bag II contains 3 white and 4 black balls
Solution:
E1 = Black ball transfer from first to second bag
E1 = White ball transfer from first to second bag
A = White ball drawn
P(E1)=59;P(E2)=49P(AE1)=38;P(AE2)=48
Using total probability theorem
 Required probability =P(E1)×P(AE1)+P(E2)×P(AE2)=59×38+49×48=1572+29=15+1672=3172

Probability exercise 30.6 question 10

Answer:
2963
Hint:
To solve this we use total probability
Given:
Bag 1 → 4 white balls ; 5 black balls
Bag 2 → 6 white balls ; 7 black balls
Solution:
P ( white ball is drawn ) =
P ( white ball transfer ) x P( white ball is drawn ) + P ( black ball transfer ) x P( black ball is drawn )
=49×714+59×614=28126+30126=58126=2963

Probability exercise 30.6 question 11

Answer:
59130
Hint:
To solve this we use
P(A)=P(E1)×P(AE1)+P(E2)×P(AE2)+P(E3)×P(AE3)
Given:
An urn contains 10 white and 3 black balls. Another urn contains 3 white and 5 black balls.
Solution:
E1=2W …{2 white balls are transferred from I to II urn}
E2=2B……{2 black balls are transferred from I to II urn}
E3=1W,1B….{A white ball and a black ball are transferred from I to II urn}
A = White ball drawn
P(E1)=10C213C2;P(E2)=3C213C2;P(E3)=10C13C113C2A= white ball P(AE1)=12;P(AE2)=310;P(AE3)=25
Using total probability theorem
 required probability =P(A)=P(E1)×P(AE1)+P(E2)×P(AE2)+P(E3)×P(AE3)=10×913×12×12+3×213×12×310+30×213×12×25=1552+3260+213=225+9+120780=354780=177390=59130

Probability exercise 30.6 question 12

Answer:
59105
Hint:
To solve this we make two case and then use total probability formula
Given:

Bag 1 – 6R + 8B

Bag 2 – 8R + 6B
Solution:
 Case 1: Red ball is transferred =614×915 Case 2: Black ball is transferred =814×815P= Case 1 + Case 2 P=614×915+814×815=54+6414×15=11814×15=118210=59105

Probability exercise 30.6 question 13

Answer:
17400
Hint:
To solve this we find the (B1, B2 and B3) then use total probability
Given:
E1: 50% Production, E2: 25% Production, E3: 25% Production
Solution:
B1 is the event when E1 produce bulbs
B2 is the event when E2 produce bulbs
B3 is the event when E3 produce bulbs
E event when a defective bulbs is selected
P(B1)=12;P(B2)=14;P(B3)=14P(EB1)=4100=125P(EB2)=4100=125P(EB3)=5100=120
Using total probability theorem,
P(E)=P(B1)×P(EB1)+P(B2)×P(EB2)+P(B3)×P(EB3)P(E)=12×125+14×125+14×120P(E)=17400


RD Sharma class 12 solutions Probability 30.6 can be a holy grail for students in their exam preparations. Chapter 30 of the NCERT will teach students about Probability. Exercise 30.6 has 13 questions that cover the concepts of conditional probability, and the Bayes theorem.

Benefits of class 12 RD Sharma chapter 30 exercise 30.6 solution for students due to the following reasons:-

  • The RD Sharma Class 12 Solutions Probability 30.6 reference book is a one-stop solution for every concept in this exercise. Many reputed institutions recommend this set of books for their students.

  • The solved sums in the RD Sharma Class 12th Exercise 30.6 are updated according to the latest NCERT syllabus. Therefore, the students will gain in-depth knowledge in the topics effortlessly.

  • The students who prepare for their exams with the RD Sharma Class 12 Solutions Probability 30.6, tend to face their exams with a higher level of confidence.

  • RD Sharma class 12th exercise 30.6 is an exceptional book for self-practice. Since students need to practice maths daily, they will be able to use these solutions to compare answers and mark themselves at home.

  • The RD Sharma Class 12th Exercise 30.6 Solutions’ PDF material can be easily accessed from the Career360 website. There is no payment received to view or download this set of solution materials.

RD Sharma Chapter-wise Solutions

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Frequently Asked Questions (FAQs)

1. Is RD Sharma class 12 chapter 30 exercise 30.6 useful for JEE mains preparations?

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