Aptitude - Probability - Discussion

Discussion :: Probability - General Questions (Q.No.6)

6. 

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

[A].
1
2
[B].
3
4
[C].
3
8
[D].
5
16

Answer: Option B

Explanation:

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.

Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
     (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
     (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n(E) = 27.

P(E) = n(E) = 27 = 3 .
n(S) 36 4


Srinivas said: (Aug 9, 2010)  
Is there any method for to solve all these type of questions?

Ranjan said: (Oct 22, 2010)  
Please discuss more about it

Sunny said: (Nov 18, 2010)  
Ya srinivas here it is
In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.

Then, not getting even no is e={(1,3)(1,5)(1,1)(3,1)(3,3)(3,5)(5,1)(5,3)(5,5)}
n(E)=9
p(E)=9/36=1/4

now probability of getting even is =1-(1/4)=3/4

Jayanna said: (Nov 23, 2010)  
This is the best method sir. the first method is confusion it will take time also . i want give u one suggestion also sir for this prob. there are 2,4,6 are even numbers in the die. for 2 ,there is 1,for 4, there is 3, and for 6 there is 5. sum of 1,3,6 equal to 9 .so 9/36=1/4 then 1-1/4=3/4

Thangamuthu said: (Dec 17, 2010)  
How it is.....? only 18 even numbers combinations are possible ....?so ans must be 1/2. .

Vara said: (Jan 18, 2011)  
For sum of numbers it is 18, for product of numbers its correct.

Phani said: (May 17, 2011)  
Provide shortcuts also with these explanations then we can able to do solve the problems very fastly.

Maruthi said: (May 17, 2011)  
Sir i am not getting probability event....three dice means how can we take the events...pls tell me.

Yaswanth said: (Jun 17, 2011)  
Is there any other questions and shortcuts regarding these problems ?

Brajesh said: (Jul 3, 2011)  
((3c1*6c1)+(3c1*3c1))/36;

Kranthi said: (Jul 27, 2011)  
1 2 3 4 5 6
---------------------

1- 2 3 4 5 6 7

2- 3 4 5 6 7 8

3- 4 5 6 7 8 9

4- 5 6 7 8 9 10

5- 6 7 8 9 10 11

6- 7 8 9 10 11 12
using this table ec can do any sort of problems
e.g; we need sun 7 means check in table that how many times it comes
it is 6 there fore 6/36

Rohan said: (Aug 7, 2011)  
P(odd) = 1/2
P(even) = 1/2
u will get an even number in three ways: odd*even
or even*odd or even * even
Hence the required probability =(1/2*1/2) +(1/2*1/2) + (1/2*1/2)
= 3*1/4
= 3/4

Anonymous said: (Mar 7, 2012)  
We can do this in the following way.

Getting an even product can be done in 3 ways

E*E=E;
E*O=E;
O*E=E;
(3C1/6C1)*(3C1/6C1)=9/36;
E*O=E;
(3C1/6C1)*(3C1/6C1)=9/36;
O*E=E;
(3C1/6C1)*(3C1/6C1)=9/36;
TOTALLY=
3*9/36= 3/4

Vassu426 said: (Oct 15, 2012)  
Dice contain 1,2,3,4,5,6 faces
from this 2,4,6 are even.
so product even is possible when,
even * even + odd * even + even * odd
so 1 has 3 chances of getting even i.e (1*2 ,1*4, 1*6)
2 has 6 chances
3 has 3
4 has 6
5 has 3
6 has 6

so total possible even products are= 3+6+3+6+3+6 => 27
ans : 27/36
=>3/4

Ram said: (Apr 27, 2013)  
Another method:

The product will only by odd if the both dies are odd. P(1st Dice is odd) = 1/2 P(2nd Dice is odd) = 1/2.

1/2 * 1/2 = p both are odd hence product is odd as both rolls are independent events. P(odd product) = 1/4

Hence p(even product) = 1 - 1/4 = 3/4.

Ch. Anusha said: (Aug 9, 2013)  
I do not understand because it is too lengthy process. Please tell the shortcuts.

Bharath. K said: (Sep 10, 2013)  
Hi @Anusha,

I will try to make you understand the concept.

Probability is n(e)/n(S). here n(S) = 6*6 = 36.

To get n(e) i.e even product, we have to multiply odd with even or even with even.

Therefore, for odd with even we get,

1*2=2(product is even).
1*4.
1*6.

Therefore 3 combinations per odd number.

Similarly (do the same with 3 and 5) we get 3*3=9 combinations
for even with even: we get,

2*1.
2*2..till 2*6.

Therefore total 6 combinations with 3 even numbers, doing the same with 4 and 6 we get 6+6+6=18 combinations. Total n(e) =odd*even+even*even=9+18.

Substituting this value in n(e)/n(s) = 27/36 or 3/4.

Chiru said: (Sep 20, 2013)  
Still it takes long time know?

I am getting concept but say in short way.

Isha said: (Feb 23, 2014)  
1st dice * 2nd dice.
Even*even = even.
Even*odd = even.
Odd*even = even.

So, 3/6 * 3/6 + 3/6 * 3/6 + 3/6 * 3/6 = (3*3*3)/(6*6) = 3/4.

Narendra said: (Jun 17, 2014)  
Hi @bharath. K.

I am not understand below line.
n(S) = 6*6 = 36.

Why we are taking 6*6?

@Pweety said: (Aug 3, 2014)  
can it be solved like this: 6*6 = 36

0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36 = 18/36 = 9/12 = 3/4.

Shraddha Pandey said: (Aug 4, 2014)  
We can simply solve this problem by firstly finding the total outcomes and then possible events according to problem.

Dhruvil said: (Aug 19, 2014)  
n(E)=9.
Total numbers on two dices = 6*6 = 36.

Number of events when the number on two dices are odd and their sum is even =3.

Number of events when the number on two dices are even and their sum is even =3.

So the probability of the sum of the number being even=(3*3/36)=(9/36). Now each dice has six numbers. So (9*6/36)=(6/4)=(3/2).

So the probability is (3/2).

Arijit said: (Aug 23, 2014)  
Two odd number makes the product odd. i.e. (1,3,5).
Probability of being the product odd is (1/2)*(1/2) = 1/4.

As we have to see only probability in getting odd numbers for 2 dices.
Probability of getting the product even is 1-(1/4) = 3/4.

Suman said: (Sep 4, 2014)  
There is a formula 7-n & 13-n. For what this formula is used?

Avhi said: (Oct 31, 2014)  
Why I'm choosing 6 number we have a another number?

Soumya said: (Jan 29, 2015)  
There is not any either easy solution? Which must not be confusing?

Nikhil said: (Apr 9, 2015)  
Sir please any one explain in a question ask product of even number but in solution shown odd number.

Ziku said: (May 10, 2015)  
Product must be a number which might be an even or an odd. So P(even/odd) = 1/2.

Shubhankar said: (Sep 1, 2015)  
Simply do.

1 = 3 times even nos (ex-1*2=2, 1*4=4, 1*6=6).
2 = 6 times.
3 = 3 times.
4 = 6 times (4*1=4, 4*2=8. Etc).
5 = 3 times even nos.
6 = 6 times.

Total times even numbers = 27; n(s) = 6*6 = 36.

Now by formula p(e) = N(E)/N(S).

27/36 = 3/4.

Sabyasachi said: (Sep 24, 2015)  
Just keep in the mind that odd is (e.g: 1, 3, 6) multiply with the even number i.e. 3 times each to make even.

And the even number is multiply with the all numbers (1, 2.6).

Solution:

1, 3, 5 (3 times each) i.e -3*3 = 9 times.

2, 4, 6 (6 times each) i.e -3*6 = 18 times.

So total favorable event-18+9 = 27.

Total no of event = 36.

So answer is = 27/36 = 3/4.

Tarunaa said: (Mar 13, 2016)  
I am unable to understand.

Please someone explain in briefly!

Adi said: (Mar 30, 2016)  
Question is what are the chances of getting two numbers whose product (multiplication) is even number (2, 4, 6).

Keisha said: (May 23, 2016)  
Probability of getting product of two numbers.

Even E= {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6), (5, 1), (5, 3,) (5, 5), (6, 2), (6, 4), (6, 6)} =18.

Total = (6 * 6) = 36.

P (E) =N (e)/N(s) = 18/36 = 1/2.

I'm confused to get the answer. Can anyone help me?

Chetana said: (Jul 21, 2016)  
You get an even number when:

Even x even.
Odd x even.
Even x odd.
Even numbers in each dice that may occur: 2, 4, 6 - Three possibilities,
Odd numbers in each dice: 1,3,5 -three possible conditions.

So even x even becomes 3 x 3 = 9.
Similarly for the other 2.
So, in total 9 + 9 + 9 = 27/36.

Prateek said: (Jul 22, 2016)  
I have the same question. Just like Keisha. Please, someone give answer.

Swathy said: (Jul 28, 2016)  
Really useful information for non-maths students like me. Thank to all.

Ashraf said: (Sep 9, 2016)  
Even = odd * even + even * even.
Odd = odd * odd oly

So in a dice odd = 1 3 5.
Another dice odd 135.

135
135 matrix e combination 9.

Odd possibility = 9/36.
Even possibility = 27/36.

Hrishi said: (Nov 15, 2016)  
@Chetana.

You explained the solution in a simple way. Great.

Andrew007 said: (Dec 9, 2016)  
Even + odd = odd.

Example: even 2 + odd 3= 5 which is odd.
So, the answer should be 1/2.

Scalar said: (Dec 11, 2016)  
Shouldn't the answer be 1/2?

The solution lists odd combinations, such as 4 and 1.

Bharath said: (Dec 29, 2016)  
@Shubhankar & @Sabyasachi.

Thanks for giving an easy method to understand.

Naren said: (Dec 31, 2016)  
It may be also a short method:

Odd no 1st dice 1, 3, 5 = 3. 2nd dice odd no 1, 2, 3 = 3 hence 3 * 3 = 9.
Therefore, the product of even no 1-9/36 = 34.

Pravin Atrekar said: (Feb 21, 2017)  
Wrong answer is mentioned here because we have to find the product not sum who's output comes even so and 9/35 =1/4.

Priya said: (Mar 22, 2017)  
@Shubhanka.

I can't understand your method. Can you explain it in detail?

Panging said: (May 12, 2017)  
How n(E) got =27?

Krishna said: (May 12, 2017)  
Sum of (4, 1), (4, 3), (4, 5) and so on in where ever even and add exit, the sum of two numbers becomes odd, but not even 4+1=5. So on with rest.

Naveena said: (Jun 7, 2017)  
I can't understand it please explain this problem.

Zaheer said: (Jun 16, 2017)  
Is there any shortcut method to solve such types of question.

Anusuya said: (Aug 29, 2017)  
I don't understand why take product why only take sum?

Please, guys explain.

Shishirkumar said: (Dec 22, 2017)  
3 cases.

even* odd=even.
even * even =even.
odd * even= even.
add all
(3/6*3/6)+3/6*3/6)+(3/6*3/6)=3/4.

Anjan Vikas Reddy said: (Jul 27, 2018)  
We can do this question in two ways:

If we are looking at how many odd ways that better and easy to think :
1,3,5 are the odd digits in dice
to get odd both numbers should be odd
so the number of chances for the first number is 3,
and for second also 3.

Because 1*1,3*3 etc are also odd.
So favourable outcomes are 3*3=9.
prob=9/36 ->odd probability,
for prob(even)= 1-prob(odd).

Haridev Purve said: (Jul 30, 2018)  
Odd * Even = Even.

Total=(3+3+3)=9;
Even*odd=even
Total=(6+6+6)=18;
So here total odd number is (1,3,5);
And even (2,4,6);
Now E=27;
And Total=6*6=36
Prob=27/37=3/4 ans.

Dipaksinh said: (Aug 26, 2018)  
First, we have to select from any of the six sides then we have only three sides even or odd so 6c1*3c1.

Then we have 3 even and 3 odd for selection so 3c1*3c1 so final.

6c1 * 3c1+3c1 * 3c1/36.

Atul Prakash said: (Jul 30, 2019)  
The simple method is : we have 3 odd number(1, 3 ,5) and 3 even number(2, 4, 6);
We know that (even* even=even): = (3 even number * 3 even number=9));
(odd* even=even):= (3 odd number * 3 even number=9);
(even*odd=even):=(3 even number * 3 odd number=9);
Total even sum=9+9+9 = 27,
Total possiblity of two dice are = 6*6 = 36 (because each dice have 6 faces),
Therefore probablity=27/36 = 3/4.


Note: Here I have taken even*odd and odd*even because either of dice may contain even or odd;i.e: 1st dice contain 1 and second will contain 2 or 1st will contain 2 and 2nd will contain 1.

T.K. Dixit said: (Jan 29, 2020)  
The answer should be 1/2.

Sameer said: (Apr 16, 2020)  
Product = multiplication of both dice number is even.

Saikiran Kiran said: (May 4, 2020)  
I am not understanding this.

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