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Probable Prime Poser (Posted on 2010-01-19) Difficulty: 2 of 5
A bag contains 10 marbles that are numbered 0 through 9. Precisely three marbles are drawn at random from the bag without replacement.

Determine the probability that a three-digit prime number (with non leading zero) can be constituted by rearrangement of digits corresponding to the three marbles (including the original order of the digits.)

As a bonus determine the corresponding probability if the three marbles were drawn with replacement at the outset.

No Solution Yet Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

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Solution computer solution to part 1 | Comment 1 of 4

There are 53 unique sets of 3 different digits that can form 3-digit primes

digits    primes
013       103
014       401
016       601
017       107 701
019       109
035       503
037       307
049       409
059       509
067       607
079       709 907
089       809
124       241 421
125       251 521
127       127 271
128       281 821
134       431
136       163 613 631
137       137 173 317
139       139 193
145       541
146       461 641
149       149 419 491 941
157       157 571 751
167       167 617 761
169       619 691
179       179 197 719 971
235       523
236       263
238       283 823
239       239 293
257       257
269       269
278       827
289       829
346       463 643
347       347 743
349       349 439
356       563 653
358       853
359       359 593 953
367       367 673
368       683 863
379       379 397 739 937
389       389 839 983
457       457 547
467       467 647
478       487
479       479 947
569       569 659
578       587 857
589       859
679       769 967

 

so that's 53 digit sets out of the C(10,3) = 120 equally likely possible sets of 3 digits chosen.

The probability is 53/120.


  Posted by Charlie on 2010-01-19 13:08:32
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