If a six-sided die is rolled three times, what is the probability that

Question

If a six-sided die is rolled three times, what is the probability that the die will land on an even number exactly twice and on an odd number exactly once?

A. 1/8

B. 1/4

C. 3/8

D. 1/2

E. 7/8

CrackverbalGMAT · Answer

Probability = Favorable Outcomes / Total Outcomes

There are 3 even numbers and e odd numbers.

P(Even Number) = 3/6 = 1/2
P(Odd Number) = 3/6 = 1/2

Probability it lands twice on an even number and once on an odd number = 1/2 * 1/2 * 1/2 = 1/8

What we must remember here is that the question does not say that the first 2 rolls are even and the 3rd roll is odd.

We must find the number of ways of getting Even, Odd Combinations which are 3!/2! = 3 (EEO, EOE, OEE)

The Required probability = 3 * 1/8 = 3/8

Option C

Arun Kumar

GMATWhizTeam · Answer

Solution 
 • Number marked on 6 faces of a fair dice are, 1, 2, 3, 4, 5, and 6.
 o So, probability of getting an even number on a roll  = \frac{3}{6} = \frac{1}{2}   
o Similarly, probability of getting an odd number on a roll  = \frac{3}{6} = \frac{1}{2}   
• Therefore, probability of getting exactly 2 even number and exactly 1 odd number on 3 rolls  =3C2* \frac{1}{2} *\frac{1}{2}*\frac{1}{2} = \frac{3}{8}  
Thus, the correct answer is  Option C.

Varunsawhney8 · Answer

We Know the Probability getting Even = 1/2 & getting odd=1/2

For exactly 2 even and 1 odd the number of arrangements can e= 3!/2!=3

Probability of getting exactly 2 even and 1 odd= 3*(1/2)^3=3/8

BrushMyQuant · Answer

Given that a fair 6-sided die is rolled three times and We need to find what is the probability that the die will land on an even number exactly twice and on an odd number exactly once?

As we are rolling three dice => Number of cases =  6^3  = 216

Now we have three places in these 3 tosses _ _ _

First of all let's find the toss in which we will get an odd number. This can happen by selecting 1 place out of 3 where odd number will come.
=> 3C1 = 3 ways

Now, Probability of getting an odd number in any toss =  \frac{3}{6}  =  \frac{1}{2}  (As 3 out of the 6 possible outcomes are odd)
Similarly, P of getting an even number =  \frac{1}{2}

=> Probability that the die will land on an even number exactly twice and on an odd number exactly once = Place of the even number * Probability of getting an odd number * Probability of getting an even number * Probability of getting an even number = 3 *  \frac{1}{2}  *  \frac{1}{2}  *  \frac{1}{2}  =  \frac{3}{8}

So,  Answer will be C 
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

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

If a six-sided die is rolled three times, what is the probability that

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