Probability of getting an AP while rolling a dice.

Probability Level 2

An unbiased dice numbered from 1 to 6 is rolled three times. What is the probability of getting an Arithmetic progression during the three rolls ?. Kindly assume that the common difference of any of these sequences is a non zero integer.

1 72 \frac1{72} 1 216 \frac1{216} 1 18 \frac1{18} 1 108 \frac1{108}

Srinivasa Gopal by Srinivasa Gopal , 53, India

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2 solutions

Parth Sankhe
Oct 23, 2018

There are 4 possible (d=1) outcomes, starting from 1 to 4. There are only 2 possible (d=2) outcomes, 135 and 246.

These six outcomes will get repeated again to give decreasing APs, thus giving us the probability as 12 6 3 = 1 18 \frac {12}{6^3}=\frac {1}{18}

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Srinivasa Gopal
Oct 23, 2018

The possible sequences which will give rise to an AP during the 3 rolls. 123 321 234 432 345 543 456 654 135 531 246 642 Total number of occurrences= 12 Total number of outcomes = 216

Probability of the three rolls giving rise to an AP is 12/216 = 6/108 = 3/54

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