With Pujara and Ishant at the crease Cricket Team of India needs to score 4 runs in last 2 balls to

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24 Mar 2017 Probability

With Pujara and Ishant at the crease Cricket Team of India needs to score 4 runs in last 2 balls to win the match. What is the probability that India doesn't 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) 9/36
3) 11/36
4) 10/35
5) 5/19
6) 4/1
7) 5/36
8) 5/18
9) 7/36
10)10/26

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
If a 4 or 6 are scored on 1st ball 2nd balls outcome doesn't matter, so actual number of possible outcomes = 36-10 = 26
Let’s assume that run scored on first ball is x and 2nd ball is y
India will not win the match if x+y <= 3.
Possible pair of values of x and y so that India doesn’t wins the match
(x, y)
(0, 0), (1, 0), (2, 0), (3, 0) , (0, 1) , (1, 1) , (2, 1) , (0, 2) , (1, 2) and (0, 3)
Count of set of values for India doesn’t wins the match = 10
Probability = Positive outcome/Total Possible Outcomes = 10/26 = 5/13
Option 10)

Correct Option: 10 Best Solution (0)