With Dhoni and Bumrah at the crease Cricket Team of India needs to score 5 runs in last 2 balls to w

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12 Dec 2017 Probability

With Dhoni and Bumrah at the crease Cricket Team of India needs to score 5 runs in last 2 balls to win the match. What is the probability that the 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) 17/36
2) 17/31
3) 16/36
4) 14/31
5) 5/12
6) 2/9
7) 15/31
8) 16/31
9) 7/12
10) None of these

Solution

On any of these 2 balls the possible runs which can be scored are: 0,1,2,3,4,6
India would win the match if India manages to score 5 or more runs in these 2 balls.

In other words India would not win the the match if India manages to score 4 or less runs in these 2 balls.
So possible pair of runs in 2 balls which will result in India losing :
(0,0), (0,1), (0,2), (0,3), (0,4), (1,0), (1,1), (1,2), (1,3), (2,0), (2,1), (2,2), (3,0), (3,1), (4,0) => count of pairs = 15

While calculating total possible outcomes, we need to take care of the fact that if 6 is hit on first ball then then second ball would not come into picture.
So total possible outcome = 6*6 - 6 + 1 = 31
Note: - 6 +1 because outcomes like (6,0), (6,1), (6,2), (6,3), (6,4), (6,6) are not valid due the fact that if 6 is scored in first ball second ball would not be bowled.
So all these 6 outcomes could be represented as 1 single outcome (6,N/A)

Probability that India would lose= 15/31
Probability that India would win= 1 - 15/31 = 16/31

Correct Option: 8 Best Solution (1)

G.S.Kantharao   7 years AGO

Possible out comes=(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)=31
Required out comes=(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,2),(3,3),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,6),(6,0)=16
Probability=16/31.
Hence my option is 8👈

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