John wrote a phone no. on a note that was later lost. John

Oldest

Best Reply

Author

Message

TAGS:

Manager

Joined: 21 Dec 2005

Posts: 107

Followers: 1

Kudos [?]: 1 [0], given: 0

John wrote a phone no. on a note that was later lost. John [#permalink]

08 Apr 2006, 19:37

John wrote a phone no. on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?

Senior Manager

Joined: 08 Sep 2004

Posts: 259

Location: New York City, USA

Followers: 1

Kudos [?]: 5 [0], given: 0

[#permalink]

10 Apr 2006, 11:47

Here is my take -

there are 7 digits : - - - - - - -

Since 1 appeared in the last three places, we now have a 4 digit number.

- - - -

What is the probability that 2 of the numbers are prime? These 4 digits can take have numbers 2 to 9. The primes are (2,3,5,7).

=> total combinations (8^4)
=> required combinations (4^2*4^2 + 4^3*4^1 + 4^4*4^0)

=> probability = 3 * 4^4 / 8^4

=> 3/16

Joined: 21 Sep 2003

Posts: 1079

Location: USA

Followers: 2

Kudos [?]: 17 [0], given: 0

[#permalink]

10 Apr 2006, 14:14

Is it 1321/2187?
P(atleast 2 primes) = 1 - {P(no primes) + P(exactly 1 prime)}

Primes = 2,3,5,7
Non-primes = 1,4,6,8,9
P{no primes} = 5*5*5*5/9^4
P{exactly 1 prime} = (4*5*5*5/9^4)*4C1 [ The given prime can occupy any 1 of the 4 places]

P(atleast 2 primes) = 1 - {625+2000}/9^4 = 1321/2187
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Joined: 29 Apr 2003

Posts: 1414

Followers: 2

Kudos [?]: 10 [0], given: 0

[#permalink]

10 Apr 2006, 16:55

4436/6561

The numbers where there are less than 2 primes (X = non primes, P = Primes)

XXXX, XXXP, XXPX, XPXX, PXXX

The probabilities for each of the above:

(625/6561) + (500/6561) + (500/6561) + (500/6561) = 2125/6561

So Probablity for all numbers where there are more than 2 prime digits:

1 - 2125/6561 = 4436/6561!

Senior Manager

Joined: 08 Sep 2004

Posts: 259

Location: New York City, USA

Followers: 1

Kudos [?]: 5 [0], given: 0

[#permalink]

14 Apr 2006, 18:47

What's the OA please?

Thanks,
Vipin

[#permalink] 14 Apr 2006, 18:47

		Similar topics	Author	Replies	Last post
Similar Topics:		John Marshall	believe2	7	04 Mar 2006, 17:26
		John Lock	vipin7um	5	19 Mar 2006, 20:58
		Having lost his sight to sustained eyestrain, John Milton	Matador	11	13 Apr 2006, 14:16
		John wrote a phone number on a note that was later lost.	cumic	5	18 May 2008, 23:16
	2	John wrote a phone number on a note that was later lost	scaredshikless	7	24 May 2010, 15:15

John wrote a phone no. on a note that was later lost. John

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

John wrote a phone no. on a note that was later lost. John

John wrote a phone no. on a note that was later lost. John

Main navigation

GMAT Resources

Partners

MBA Resources