M4maths Previous Puzzles

02 Nov 2017 Probability

With Dhoni and Bhuvi at the crease Cricket Team of India needs to score 7 runs in last 2 balls to win the match. What is the probability that the match would be a tie? 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) 1/9
2) 1/6
3) 11/36
4) 10/35
5) 1/3
6) 2/9
7) 5/36
8) 5/18
9) 7/36
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
It would be a tie match if India manages to score exactly 6 runs in these 2 balls.

So possible pair of runs in 2 balls which will result in a tie :
(6,0), (4,2), (2,4), (3,3), (0,6) => count of pairs = 5

Probability that it would be a tie = 5/36

Correct Option: 7 Best Solution (3)

~Sandeep~   7 years AGO

Total Possible outcomes = 6*6 = 36

Positive Outcomes for a tie = (3,3) (4,2) (2,4) (6,0) (0,6)
Count of positive outcomes = 5

So required probability = 5/36

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Smriti shikha   7 years AGO

the possible combination for getting a tie is (0,6) (6,0) (2,4) (4,2) (3,3) = 5
total no of combination = 36
ans=5/36

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ashok pittu   7 years AGO

ans should be 5/36.
possible outcomes are,
(1,0) (2,0) (3,0) ................
(1,1) (2,1) (3,1) ................
(1,2) (2,2) (3,2) ................
(1,3) (2,3) (3,3) ................
(1,4) (2,4) (3,4) ...............
(1,5) (2,5) (3,5) ...............
(1,6) (2,6) (3,6) ...............
finally total outcomes are 36 including 0's in both two balls.
our required outcomes are (3,3) (4,2) (2,4) (6,0) (0,6)
The total number of possible ways are 5
so, The probability to tie a match is 5/36

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