It is currently 28 Jun 2017, 00:55

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If a fair dice is rolled three times, what is the

Author Message
Manager
Joined: 27 Aug 2004
Posts: 124
Location: US
If a fair dice is rolled three times, what is the [#permalink]

### Show Tags

02 Sep 2004, 18:11
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If a fair dice is rolled three times, what is the probability that the product of the numbers rolled is even?
Intern
Joined: 31 Aug 2004
Posts: 23

### Show Tags

02 Sep 2004, 18:22
Product will be even when atleast one roll gives E...ie either 1E n 2Odds....2E n 1 O...or 3 E

1E 2O=(1/2)*(1*2)*!1/2)*3......coz 3 ways....EOO,OEO,OEE(in 3 throws)...=3/8

2E 1O=3/8 as above

3E=1/8

so prob that prod is E=(3/8)+(3/8)+(1/8)=7/8

did i go wrong.....OA plz!
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4288

### Show Tags

02 Sep 2004, 19:35
I somehow read that 3 dice were thrown 3 times at first
I got 1/2
Product will be odd whenever we have 1 or 3 odd dice
This sums up to
(1/2)^3 * 3C1 + (1/2)^3 * 3C3
1/8 * 3 + 1/8 * 1
3/8 + 1/8 = 1/2
Prob of even sum is 1 - 1/2 = 1/2

When you think of it, the choices you have for odd/even dice are:
OOE
EEO
EEE
OOO

Basically, no calculation is really needed as you have half the chance out of all possibilities to have 1 odd and 3 odd
_________________

Best Regards,

Paul

Intern
Joined: 31 Aug 2004
Posts: 23

### Show Tags

02 Sep 2004, 23:34
I donno i still feel it is 7/8.......prod of the 3 nos is supp to be Even...........i.e. ATLEAST One throw has to show an even number........which is 1- Probability of 3 Odds.....which is again 1/(1/8)=7/8..........
Director
Joined: 20 Jul 2004
Posts: 592

### Show Tags

02 Sep 2004, 23:35
pb that the product is even
= 1 - pb that the product is odd
= 1 - pb that all the three entries were odd
= 1 - 1/2 x 1/2 x 1/2
= 7/8
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

### Show Tags

02 Sep 2004, 23:47
Possibilites is EOO
EEO
EEE
OOO

P(E) = 1/2
P(O) = 1/2

P(E) and P(O) are independent events.

So P(EOO) = 1/8
P(EEO) = 1/8
P(EEE) = 1/8
P(OOO) = 1/8

All 4 events are not mutually exclusive, so we can just add them up.

P(Product is even) = 1/2
Director
Joined: 20 Jul 2004
Posts: 592

### Show Tags

02 Sep 2004, 23:52
hardworker_indian wrote:
pb that the product is even
= 1 - pb that the product is odd
= 1 - pb that all the three entries were odd
= 1 - 1/2 x 1/2 x 1/2
= 7/8

Oops, I forgot that one odd dice could also end up in odd product. Paul's explanation says it all. Ans should be 1/2
Manager
Joined: 18 Jun 2004
Posts: 103
Location: san jose , CA

### Show Tags

03 Sep 2004, 01:28
I don't know if my way of solvingth eproblem is right or wrong .

If 1 of the 3 outcome is even , then obviously the product is even .

first time P(Even) = 3/6 = 1/2
second P(Any) = 6/6 = 1
Third p(Any) = 6 /6

1/2 * 1* 1 = 1/2
_________________

---- Hero never chooses Destiny
Destiny chooses Him ......

Intern
Joined: 02 Sep 2004
Posts: 35

### Show Tags

03 Sep 2004, 02:35
Rahul - you are mistaken in assuming that even number will be rolled only the first time around.

Now you have rightly assumed that prob. of even number rolling out the first time is 1/2.
BUT - when the odd number is rolled the first time around - the probability is 1/2...in that case ALSO we may get a even number if an even number is rolled either the second or the third time. So we got to add to the answer you got....

Thus the probability according to your method is
1/2 x 1 x 1 = 1/2 as you calculated plus - 1/2 x 1/2 x 1 (Even second time). plus 1/2 x 1/2 x 1/2 (even 3rd time but not second time)

Thus the total is - 4/8 plus 2/8 plus 1/8 = 7/8. Hope this helps....
_________________

To be or not to be....

Director
Joined: 31 Aug 2004
Posts: 606

### Show Tags

03 Sep 2004, 02:59
P= 1 - Probability to have no even number in the 3 rolls.

No even = 1/2.1/2.1/2=1/8

so P=7/8
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4288

### Show Tags

03 Sep 2004, 05:03
twixt wrote:
P= 1 - Probability to have no even number in the 3 rolls.

No even = 1/2.1/2.1/2=1/8

so P=7/8

You also have to substract the probability of "2 even numbers" because when you have 1 odd die, the product will also be odd
_________________

Best Regards,

Paul

Manager
Joined: 27 Aug 2004
Posts: 124
Location: US

### Show Tags

03 Sep 2004, 07:35

Anyone would like to explain it.
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4288

### Show Tags

03 Sep 2004, 08:56
Hmm, basic mistake How could I assume that odd*even*even (4*2*1 = 6 --> even!) will give an odd?! 7/8 it is.
_________________

Best Regards,

Paul

03 Sep 2004, 08:56
Display posts from previous: Sort by