Two fair six-sided dice, each numbered 1 to 6, are rolled once. What

Question

Two fair six-sided dice, each numbered 1 to 6, are rolled once. What is the probability of getting exactly one even numbers ?

A. 3/5
B. 1/2
C. 1/3
D. 3/10
E. 1/4

gmatophobia · Answer

The below combinations are possible -

1) Even on first dice & odd on second dice
2) Odd on first dice & even on second dice

Even on first dice & odd on second dice

Required Probability =  \frac{3}{6}  *  \frac{3}{6}

Odd on first dice & even on second dice

Required Probability =  \frac{3}{6} * \frac{3}{6}

Total Probability =  2 * (\frac{1}{2} * \frac{1}{2}) = \frac{1}{2}

Iotaa · Answer

Possible outcome- 1,2,3,4,5,6. Probability of getting an even number= 3/6=1/2

So for exactly 1 even, either it should come in 1st dice or in 2nd.

Even in 1st Dice X Odd in 2nd dice + Odd in 1st dice + even in 2nd; 1/2 X 1/2 + 1/2 + 1/2 = 1/2

Option B is the answer

ThatDudeKnows · Answer

EvenEven
EvenOdd
OddEven
OddOdd

Each of those is equal probability.

2/4 = 1/2

Answer choice B.

BrushMyQuant · Answer

Method 1: Logic   
 
 Two fair six-sided dice, each numbered 1 to 6, are rolled once. What is the probability of getting exactly one even numbers ?

As we are rolling two fair dice so there is equal probability of getting any of the following cases
(E,E), (E,O), (O,E), (O,O) where O is Odd and E is Even

P(Getting exactly one even number)  = Probability of getting (E,O), (O,E) =  \frac{2}{4}  =  \frac{1}{2}

Method 2: Algebra

Two fair six-sided dice, each numbered 1 to 6, are rolled once.

As we are rolling 2 dice => Number of cases =  6^2  = 36

What is the probability of getting exactly one even numbers ?

P(exactly one even number) = P(Even in 1st and Odd in 2nd) + P(Odd in 1st and Even in 2nd) =   \frac{1}{2}  *  \frac{1}{2}  +  \frac{1}{2}  *  \frac{1}{2}  =  \frac{1}{4}  +  \frac{1}{4}  =  \frac{1}{2}

So,  Answer will be B 
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

Two fair six-sided dice, each numbered 1 to 6, are rolled once. What

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