M4maths Previous Puzzles

27 Jan 2017 Probability

With Dhoni and Yuvraj at the creaseCricket Team of India needs to score 9 runs in last 2 balls to win the match. What is the probability that India wins the match? Assume that:
- There were no wide balls or no balls bowled in these 2 balls.
- No Wicket has fallen in these 2 balls
- No Overthrows or extra runs were scored in these 2 balls
- In case if run(s)are scored on any of these 2 balls it can only be one of these values: 1, 2, 3, 4 & 6
This also implies that it’s quite possible that zero runs are scored on a particular ball

OPtion

1) 1
2) 1/6
3) 1/9
4) 1/9
5) 1/4
6) 1/36
7) 3/36
8) 5/36
9) 7/36
10)8/36

Solution

On any of these 2 balls the possible runs which can be scored are: 0,1,2,3,4,6
So total possible number of runs which can be scored in 2 balls are = 6C1*6C1 = 36
Let’sassume that run scored on first ball is x and 2nd ball is y
To win the match x+y>= 9. Possible pair of values of x and y are:
(x, y)
(4, 6), (6, 4), (6, 3), (3, 6) and (6, 6)
Count of set of values for India to win the match = 5
Probability = Positive outcome/Total Possible Outcomes = 5/36
Option 8)

Correct Option: 8 Best Solution (12)

G.S.Kantharao   7 years AGO

Total out comes are = 6*6=36
Suitable out comes (3,6),(6,3),(4,6),(6,4),(6,6)=5
Probability of winning=5/36
Hence my option is 8.

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DHANANJAY KUMAR   7 years AGO

possible runs chances are 0,1,2,3,4,6 then total no of pair are 36
then required run is 9 then there are 5 possible ways (6,6),(6,4),(6,3),(4,6),(3,6)
then probability=5/36

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saidinesh   7 years AGO

the possible : (3,6),(6,3),(6,6),(6,4),(4,6)= 5 sases
therefore, total sases=36
==>5/36 c is not working so i used s

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SATHEESH V   7 years AGO

(6,6),(6,4),(6,3),(4,6),(3,6) ..........5 possibilities to win
total possiblities = 6*6=36

probability=5/36

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Ajay Sharma   7 years AGO

total number of possible out come for first ball=6
total number of possible outcome for second ball=6
so, total possible distinct outcome=6*6=36
outcome which results 9 or more run=(3,6)(4,6)(6,3)(6,4)(6,6)=5
so probability of india winnin match is 5/36

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namesh   7 years AGO

total possibilities = 36
favourable outcome = 5 {(6,6),(6,4),(6,3),(4,6),(3,6)}

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amit kumar   7 years AGO

no of ways to get 9 runs (from last 2 balls)=(6,3),(3,6),(4,6),(6,4),(6.6)=5 total no of possible ways=6*6=36
P(win)=5/36

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Idemakanti Madhuri   7 years AGO

Total there are 5 chances to win by using 1,2,3,4 and 6 points getting in any one of two balls.that is either((6,3),(6,4),(6,6)) or ((3,6),(5,6),(6,6)).so in all those (6,6) is repeated so total 5chances to win..in the questions it needs 9 to win but greater than 9 also win..i,e atleat 9 need to win

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sruthi pujari   7 years AGO

Probability of winning is getting score>9 it means
(6,6),(6,4),(6,3),(3,6),(4,6) =>5possibilities in two balls
Total 0,1,2,3,4,6 =36 possibilities.
Prob=5/36

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Basant Bothra   7 years AGO

Runs in 2 balls can be any of the following:
(0,0),(0,1),(0,2),(0,3),(0,4),(0,6),
(1,0),(1,1),(1,2),(1,3),(1,4),(1,6),
(2,0),(2,1),(2,2),(2,3),(2,4),(2,6),
(3,0),(3,1),(3,2),(3,3),(3,4),(3,6),
(4,0),(4,1),(4,2),(4,3),(4,4),(4,6),
(6,0),(6,1),(6,2),(6,3),(6,4),(6,6).
answer will be=5/36

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Gaurav Arora   7 years AGO

Total possible combinations are 36,out of these 5 are winning combinations like (6,6), (4,6)...etc
so 5/36 is answer

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Mukund Manohar   7 years AGO

Total Possible Outcome = 6C1 * 6C1 = 36
Positive Outcome = (3,6),(4,6),(6,3),(6,4) and (6,6) = 5
Required Probability = Positive Outcome / Total Possible Outcome
= 5/36

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