Probability for Business Management Simplified
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PROBABILITY FOR BUSINESS MANAGEMENT SIMPLIFIED
by : DR. T.K. JAIN AFTERSCHO☺OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india for PGPSE participants PGPSE : FREE FOR ALL, OPEN FOR ALL mobile : 91+9414430763
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 1
WHAT IS EXCLUSIVE EVENT?
WHEN RESULTS FROM SOME EXPERIMENT ARE SUCH THAT IF ONE OUTCOME (EVENT) HAPPENS, OTHERS ARE IMPOSSIBLE, THEN THEY ARE CALLED EXCLUSIVE EVENTS. FOR EXAMPLE, IF YOU TOSS A COIN, YOU CAN GET EITHER HEAD OR TAIL – NOT BOTH - THESE ARE EXCLUSIVE EVENTS
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 2
WHAT IS PROBABILITY ?
FINDING THE POSSIBILTY OF AN EVENT OUT OF MANY EQUALLY LIKELY EVENTS IS CALLED PROBABILITY THUS IF YOU THROW A COIN, THE PROBABILITY OF GETTING HEAD IS ½ BECAUSE THERE ARE 2 EQUALLY LIKELY EVENTS AND ONE HEAD.
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 3
What is exhaustive list of events?
All the possibilities are called exhaustive list. For example : coin has two possibilities : head and tail – thus these two are exhaustive - there is no other possibilitiy
5 DECEMBER 09
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Q : what is the probability of getting 2 heads out of 3 tosses of coins?
First : list down all the possibilities : H= Head, T=tail we may have all heads : HHH, we may have all tail : TTT : 1. HHH 2 TTT 3 HTH 4 THT 5 HHT 6 HTT 7 TTH 8 THH in simple terms : 2^3 = 8 possibilities : (the formula is options ^ number of trials) out of these the cases of 2 heads are : 3/8 answer
5 DECEMBER 09
AFTERSCHOOOL centre for social entrepreneurship bikaner
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What is the possibility of getting a difference of 2 when you toss a dice twice?
Let us list down all the possibilities : (1,1) (1,2)(13)(1,4)(1,5),(1,6),(2,1),(2,2),(2,3), (2,4), (2,5), (2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3), (4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1), (6,1),(6,2),(6,3),(6,4),(6,5),(6,6) there are total 36 possibilities out of which, 8 cases involve difference of 2, so answer : 8/36
5 DECEMBER 09
AFTERSCHOOOL centre for social entrepreneurship bikaner
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What is the chance of picking up a spade or an ace from a pack of cards?
There are 13 spade cards. There are 4 ace cards. Thus there are 13+4 cards = 17 out of which one ace+spade is included thus we have 16 out of 52 possibilities : 16/52 answer
5 DECEMBER 09
AFTERSCHOOOL centre for social entrepreneurship bikaner
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What is the probability that a committee of 7 persons has 5 men and 2 women, it is to be formed out of 8 men and 5 ladies
We have to pick up 7 persons out of (8+5) = 13 members so the total possibilities are : 13C7 = 13! / (7! * (13-7)!) =13*12*11*10*9*8*7*6*5*4*3*2*1/ (7*6*5*4*3*2*1*6*5*4*3*2*1) =1716 methods of selecting 5 men and 2 women : 8C5 * 5C2 = (8*7*6/3*2*1) (5*4/2*1) = 560 answer = 560/1716 answer
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 8
A number is picked up out of 25 natural numbers, what is the probability that it is divisible by 4?
Out of 25 number, there are 6 numbers divisible by 4 : 4,8,12,16,20,24 thus the probability is : 6/25 answer
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AFTERSCHOOOL centre for social entrepreneurship bikaner
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P (A-B) = 1/5 and P(A)=1/3 and P(B)=1/2, what is the probability that out of A and B, only B will happen?
P(A-B) = P(A) (1/3)– (P(A intersection B) = 1/5 thus P(A intersection B)= 1/3-1/5= 2/15 we want P (B-A) = P(B)-P(A intersection B) =1/2 – 2/15 = 11/30 ans.
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 10
A hits 5 out of 9 correct shots and B hits 6 out of 11 correct, what is the probability that when they try they are able to hit correct?
First find out the possibility that target is NOT hit at all : A not hitting : (1-5/9) = 4/9 A = 4/9 and B = 5/11 A *B = 4/9 * 5/11 = 20/99 thus they will hit : 1-20/99 = 79/99 answer
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 11
8 balls are distributed at random among 3 boxes, what is the probability that the first box will get 3 balls?
8 balls can be distributed to 3 boxes in 3^8 manners. We want first box to have 3 balls, so 8C3, now we have 5 balls left out which have to be distributed to remaining 2 boxes : 2^5 answer : (8C3*2^5)/3^8 = 1792/6561 answer
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 12
Odds in favour of an event is 2:3 and odds against another event is 3:7 ,what is the probability that at least one of these will happen
First event : happening : 2/5 not happening : 3/5, 2nd event happen : 7/10 and not happen : 3/10 Find the probability that none of these happen : 3/5 * 3/10 = 9/50 at least one of them will happen is : 1-9/5 =41/50 answer
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THANKS....
GIVE YOUR SUGGESTIONS AND JOIN AFTERSCHOOOL NETWORK / START AFTERSCHOOOL NETWORK IN YOUR CITY [email protected] PGPSE – WORLD'S MOST COMPREHENSIVE PROGRAMME IN SOCIAL ENTREPRENEURSHIP
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by : DR. T.K. JAIN AFTERSCHO☺OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india for PGPSE participants PGPSE : FREE FOR ALL, OPEN FOR ALL mobile : 91+9414430763
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 1
WHAT IS EXCLUSIVE EVENT?
WHEN RESULTS FROM SOME EXPERIMENT ARE SUCH THAT IF ONE OUTCOME (EVENT) HAPPENS, OTHERS ARE IMPOSSIBLE, THEN THEY ARE CALLED EXCLUSIVE EVENTS. FOR EXAMPLE, IF YOU TOSS A COIN, YOU CAN GET EITHER HEAD OR TAIL – NOT BOTH - THESE ARE EXCLUSIVE EVENTS
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 2
WHAT IS PROBABILITY ?
FINDING THE POSSIBILTY OF AN EVENT OUT OF MANY EQUALLY LIKELY EVENTS IS CALLED PROBABILITY THUS IF YOU THROW A COIN, THE PROBABILITY OF GETTING HEAD IS ½ BECAUSE THERE ARE 2 EQUALLY LIKELY EVENTS AND ONE HEAD.
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 3
What is exhaustive list of events?
All the possibilities are called exhaustive list. For example : coin has two possibilities : head and tail – thus these two are exhaustive - there is no other possibilitiy
5 DECEMBER 09
AFTERSCHOOOL centre for social entrepreneurship bikaner
4
Q : what is the probability of getting 2 heads out of 3 tosses of coins?
First : list down all the possibilities : H= Head, T=tail we may have all heads : HHH, we may have all tail : TTT : 1. HHH 2 TTT 3 HTH 4 THT 5 HHT 6 HTT 7 TTH 8 THH in simple terms : 2^3 = 8 possibilities : (the formula is options ^ number of trials) out of these the cases of 2 heads are : 3/8 answer
5 DECEMBER 09
AFTERSCHOOOL centre for social entrepreneurship bikaner
5
What is the possibility of getting a difference of 2 when you toss a dice twice?
Let us list down all the possibilities : (1,1) (1,2)(13)(1,4)(1,5),(1,6),(2,1),(2,2),(2,3), (2,4), (2,5), (2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3), (4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1), (6,1),(6,2),(6,3),(6,4),(6,5),(6,6) there are total 36 possibilities out of which, 8 cases involve difference of 2, so answer : 8/36
5 DECEMBER 09
AFTERSCHOOOL centre for social entrepreneurship bikaner
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What is the chance of picking up a spade or an ace from a pack of cards?
There are 13 spade cards. There are 4 ace cards. Thus there are 13+4 cards = 17 out of which one ace+spade is included thus we have 16 out of 52 possibilities : 16/52 answer
5 DECEMBER 09
AFTERSCHOOOL centre for social entrepreneurship bikaner
7
What is the probability that a committee of 7 persons has 5 men and 2 women, it is to be formed out of 8 men and 5 ladies
We have to pick up 7 persons out of (8+5) = 13 members so the total possibilities are : 13C7 = 13! / (7! * (13-7)!) =13*12*11*10*9*8*7*6*5*4*3*2*1/ (7*6*5*4*3*2*1*6*5*4*3*2*1) =1716 methods of selecting 5 men and 2 women : 8C5 * 5C2 = (8*7*6/3*2*1) (5*4/2*1) = 560 answer = 560/1716 answer
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 8
A number is picked up out of 25 natural numbers, what is the probability that it is divisible by 4?
Out of 25 number, there are 6 numbers divisible by 4 : 4,8,12,16,20,24 thus the probability is : 6/25 answer
5 DECEMBER 09
AFTERSCHOOOL centre for social entrepreneurship bikaner
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P (A-B) = 1/5 and P(A)=1/3 and P(B)=1/2, what is the probability that out of A and B, only B will happen?
P(A-B) = P(A) (1/3)– (P(A intersection B) = 1/5 thus P(A intersection B)= 1/3-1/5= 2/15 we want P (B-A) = P(B)-P(A intersection B) =1/2 – 2/15 = 11/30 ans.
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 10
A hits 5 out of 9 correct shots and B hits 6 out of 11 correct, what is the probability that when they try they are able to hit correct?
First find out the possibility that target is NOT hit at all : A not hitting : (1-5/9) = 4/9 A = 4/9 and B = 5/11 A *B = 4/9 * 5/11 = 20/99 thus they will hit : 1-20/99 = 79/99 answer
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 11
8 balls are distributed at random among 3 boxes, what is the probability that the first box will get 3 balls?
8 balls can be distributed to 3 boxes in 3^8 manners. We want first box to have 3 balls, so 8C3, now we have 5 balls left out which have to be distributed to remaining 2 boxes : 2^5 answer : (8C3*2^5)/3^8 = 1792/6561 answer
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 12
Odds in favour of an event is 2:3 and odds against another event is 3:7 ,what is the probability that at least one of these will happen
First event : happening : 2/5 not happening : 3/5, 2nd event happen : 7/10 and not happen : 3/10 Find the probability that none of these happen : 3/5 * 3/10 = 9/50 at least one of them will happen is : 1-9/5 =41/50 answer
5 DECEMBER 09 AFTERSCHOOOL centre for social entrepreneurship bikaner 13
THANKS....
GIVE YOUR SUGGESTIONS AND JOIN AFTERSCHOOOL NETWORK / START AFTERSCHOOOL NETWORK IN YOUR CITY [email protected] PGPSE – WORLD'S MOST COMPREHENSIVE PROGRAMME IN SOCIAL ENTREPRENEURSHIP
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