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

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..........

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

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

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

I don't know if my way of solvingth eproblem is right or wrong .
Please correct me guys .

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

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....

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

7/8 - is the answer.

Anyone would like to explain it.

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