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Business data analyst ii Interview Questions


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Phone Interview #2 You are playing a game of baseball. There are two outs in the bottom of the ninth, and you are down by one run. You are currently a baserunner on first base. [Obviously, you must score or else the game ends]. A)You are trying to figure out if you should steal second base or not. What kind of information do you need to know to inform this decision? B) Every batter in your lineup has identical odds.They get a single 50% of the time and they strike out 50% of the time. If you are on first base, you cannot score on a single. If you are on second, you are guaranteed to score on a single. You successfully steal 75% of the time. Should you steal? [I may be missing some of the nonsense here, but this is all the relevant information] C) It turns out the pitcher acts a bit differently with a runner on second [regardless of who the batter is] and no other runners on base. Under these circumstances, he is 50% to strike them out, 40% to surrender a walk, and 10% to surrender a hit. How does this change things/ should you steal?

3 Answers

A) Ultimately, you need to know the odds of you scoring without stealing, the odds of you scoring if you successfully steal, and the odds of successfully stealing. There are other factors, but this is what it all ultimately boils down to. B) Odds of you scoring when attempting to steal are .75*.5 = .325. Odds of you scoring waiting for two successful base hits [whats required] are .5*.5 =.25. You should steal. C) You're still .25 to score hoping for two hits in a row. Stealing now changes the equation to .75(.1+.4(.5)) because you need steal+hit or steal+walk+hit = .75(.3) = .225. You should not steal.

(C) is not as straightforward as the previous answer suggests. After a hit, are you on 3rd or 2nd? How does that change the probability for the pitcher/hitter? All things considered, you should still steal. You have the following scenarios in which you score: Steal&Hit or Steal&Walk&Hit or Steal&Walk&Walk&Hit or Steal&Walk&Walk&Walk. In all of these scenarios, a runner reaches 2nd, so our new probabilities are used. The final prob should be %16.5. If you don't steal, you have these scenarios: Hit(.50 prob) &Hit(.10 prob assuming 2nd & 3rd baserunners have same impact) or Hit&Walk&Hit or Hit&Walk&Walk&Hit or Hit&Walk&Walk&Walk. This yields prob of %11, given that baserunners in scoring position are the cause of the new probability, not just on second. Again, these would be things to clarify in the interview

To the more recent post: No the original answer is correct. If there's a hit the runner from 2nd scores, a runner on 1st goes to 2nd. There's no such thing as a Steal-Walk-Walk because this pitcher's oddity only applies when there's a runner on 2nd and nobody else on base.

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