Two six-sided dice, each numbered from 1 to 6, are rolled, and the

Question

Two six-sided dice, each numbered from 1 to 6, are rolled, and the numbers appearing are then multiplied. What is the probability that the resulting product is even?

A. 1/4
B. 1/2
C. 2/3
D. 3/4
E. 5/6

gmatophobia · Answer

Probability(even) = 1 - P(odd)

The probability that the product is odd is when both the numbers on the dice are odd.

P(odd on Dice 1) =  \frac{3}{6}

P(odd on Dice 2) =  \frac{3}{6}

P(odd on Dice 1 & Dice 2) =  \frac{3}{6} * \frac{3}{6} = \frac{1}{4}

Probability(even) =  1 - \frac{1}{4} = \frac{3}{4}

Option D

iipshitaaaa · Answer

Ways to get an odd product - odd * odd

Total possibilities for odd product :
1,3,5 & 1,3,5 
3*3=9 ways

Total outcome = 6*6 
P( odd products ) = 9/36 = 1/4

P( even products ) = 1-1/4= 3/4

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JoeKan1234 · Answer

P(E*E)=(3/6)(3/6)=1/4

P(O*E)=2!*(3/6)(3/6)=1/2

P(product is even)=1/4+1/2=3/4

BrushMyQuant · Answer

Method 1: Logic

As we are rolling two dice so there can be following cases 
 (E,E), (E,O), (O,E), (O,O) where E-> Even, O-> odd

Since, the dice are fair so there is an equal chance of following 4 cases.
To get a product as an Even number we can have three cases (E,E), (E,O), (O,E)

=> P(Product=Even) =  \frac{3}{4}

Method 2: Algebra

P(Product = Even) = 1 - P(Product = Odd)

To get an odd number we need to get odd in both the cases

=>  P(Product = Odd)  = P(Odd in  1^{st}  die) * P(Odd in  2^{nd}  die) =  \frac{1}{2}  *  \frac{1}{2}  =  \frac{1}{4} 
( as we have six number (1,2,3,4,5,6) and we have equal probability of getting an even or an odd number)

=>  P(Product = Even)  = 1 -  \frac{1}{4}  =  \frac{3}{4}

So,  Answer will be D 
Hope it helps!

Playlist on Solved Problems on Probability  here

Watch the following video to MASTER Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

aashnaag · Answer

“Resulting 4 numbers are consecutive - doesn’t that mean that it’s asking for the probability of the numbers being arranged consecutively? What am I missing here?

Krunaal · Answer

Not sure what you're referring to. In the question it is only mentioned " resulting product is even "

Two six-sided dice, each numbered from 1 to 6, are rolled, and the

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