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CMI CS 2025 | Part A | Question: 7

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Rohit Sharma is facing Shardul Thakur's bowling in the IPL. $40 \%$ of Shardul's deliveries to Rohit are good length balls, $40 \%$ are short pitched, and $20 \%$ are overpitched. Rohit hits a boundary $40 \%$ of the time off good length balls, and $80 \%$ of the time off short pitched and overpitched balls. Given that Rohit has hit a boundary off Shardul's last ball, what is the probability that it was short-pitched?

  1. $1 / 4$
  2. $1 / 3$
  3. $1 / 5$
  4. $1 / 2$

3 Answers

0 0 votes
Option D is the correct answer.

B  = Hitting a boundary

GL = good length delivery

SP = short pitched delivery

OP = over pitched delivery

from the given question

P(GL) = 0.4 , P(SP)  = 0.4 , P(OP) = 0.2

P(B|GL) = 0.4 , P(B|SP) = 0.8 , P(B|OP) = 0.8

P(SP,B) = P(B|SP)*P(SP) which is 0.4*0.8 = 0.32

To find P(SP|B) we can easily find this using Bayes Therorem we just need to find out the marginalized probability of hitting a boundary

P(B) = P(B|SP)*P(SP) + P(B|OP)*P(OP) + P(B|GL)*P(GL)

P(B) = 0.4*0.80 + 0.2*0.8 +0.4*0.4 = 0.64

P(SP|B) = P(SP,B) / P(B) = 0.32 / 0.64 = 1 / 2 , therefore OPTION D
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