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Matleena chooses three numbers at random from the numbers 1, 2, 3,..., 10. What is the probability that they are not all consecutive? (For example, the three numbers 6, 7, 8 are consecutive.)

rohitaop  Jun 12, 2018
#1
+1

This is my understanding of this problem:

There are the following consecutive possibilities:

123, 234, 345, 456, 567, 678, 789, 8910. Or 8 possibilities.

The probability of any of the above combination is:

1 x 1/9 x 1/8 =1/72

1/72 x 8 =8/72 = 1/9 probability of drawing 3 consecutive numbers. Therefore:

1 - 1/9 =8/9 probability of drawing 3 non-consecutive numbers.

P.S. Somebody should check this!.

Guest Jun 13, 2018
edited by Guest  Jun 13, 2018
#2
+92873
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Thanks guest, probability is always tricky.

Matleena chooses three numbers at random from the numbers 1, 2, 3,..., 10. What is the probability that they are not all consecutive? (For example, the three numbers 6, 7, 8 are consecutive.)

If the order they are drawn counts then

Number of possible permutations is 10*9*8 and the number of consecutive combinations is 8

so the probability that they ARE consceutive is  8/(8*9*10) = 1/90

and the probability that they are NOT consecutive is 89/90

If the order they are draw does NOT count then  234 is the same as 324 and this is different

Number of possible combinations is 10C3 = 120

The number of consecutive combinations is still 8

So the prob of getting three consecutive numbers is 8/120 = 1/15

The probability that they are not consecutive is 14/15

Melody  Jun 18, 2018