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A man can take a step forward, backward, left or right with equal probability. Find the probability that after nine steps he will be just one step away from his initial position.

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Important Questions on Probability

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Quantum CAT Also Useful for XAT>Chapter 20 - SNAP>CMAT>Q 18
Urn A contains 6 red and 4 black balls and urn B contains 4 red and 6 black balls. One ball is drawn at random from urn A and placed in urn B. Then, one ball is drawn at random from urn B and placed in urn A. If one ball is drawn at random from urn A, the probability that it is found to be red, is equal to _____
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Quantum CAT Also Useful for XAT>Chapter 20 - SNAP>CMAT>Q 19
The digits 1, 2, 3, …, 9 are written in random order to form a nine digit number. Find the probability that this number is divisible by 11.
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Quantum CAT Also Useful for XAT>Chapter 20 - SNAP>CMAT>Q 20
A terror outfit, works under the pseudonym of Mafia Wars, uses 12 satellite phones, during its operation to communicate with each other. Each of the 12 terrorists is armed with a satellite phone, an AK-47 and hand grenades among other explosives. Except the four terrorists, who are hidden in a tiny staff washroom of a prominent hotel, no two terrorists are positioned at the same location. The terrorists who are hidden in the washroom are codenamed as Alpha and the ones who are hidden at other surrounding locations are codenamed as Beta. Due to location differences Beta terrorists cannot communicate without the satellite phone, at all. In order to speak to any of the Alpha terrorist a Beta terrorist can call on any one of the phones available with Beta, similarly to speak to any Beta terrorist an Alpha can call from any one of the phones available with them. A conference call can be made between any three satellite phones. If three phones are chosen randomly from the 12 phones, then what is the probability that the terrorists can make a conference call?
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Quantum CAT Also Useful for XAT>Chapter 20 - SNAP>CMAT>Q 21
Zuckerberg, my Facebook friend, recently returned from his honeymoon trip to three European cities - Paris, Milan and Zurich, where he had clicked some photos before uploading them on Facebook in three different folders naming them on the cities he had visited. The folders Paris, Milan and Zurich have 3, 4, and 5 photos, respectively. He asks his six-year-old niece Olivia Bee that if she could download these photos and edit them using Instagram and put them back but only one photo in each folder. Within no time she edits all the photos and uploads back quickly one photo in each folder. What's the probability that she uploads at least two photos of the same city and no folder has the photo uploaded back to its original folder, after editing?
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Quantum CAT Also Useful for XAT>Chapter 20 - SNAP>CMAT>Q 22
In a regular decagon, there are diagonals of distinct sizes. If all the possible diagonals are drawn and you choose any one diagonal at random then what is the probability that it is neither the shortest one nor it is the longest one?