A fair, six-sided die is rolled three times. What is the probability

Probability that a roll will be even = 3/6 = 1/2

Number of favorable outcomes = 3 (EOO, OEO, OOE)

Probability that exactly one roll is even = (1/2)*(1/2)*(1/2)*3 = 3/8 = 0.375

Answer is (D)
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2,4,6 among 1,2,3,4,5,6
Probability of getting an even number is=3c1/6c1=1/2
Probability of not getting an even number is 1-1/2=1/2
On the first die even ,second odd, third odd
1/2*1/2*1/2=1/8
This can happen in three ways as even can come on die 2(Not on1 Not On 3) and 3(not on 1 not on 2) as well
So required probability=3/8
0.375
D:)

even=2,4,6
odd=1,3,5

1. Even number= Ist digit (even)*2nd digit(odd)*3rd digit(odd)=3*3*3=27
2. Even number= Ist digit (odd)*2nd digit(even)*3rd digit(odd)=3*3*3=27
3. Even number= Ist digit (odd)*2nd digit(odd)*3rd digit(even)=3*3*3=27


=81

Total number of events= 6*6*6=216

Required probability= 81/216= 0.375

IMO D

We can use the Formula

=nCr * P^r * (1-P)^(n-r)

= 3C1 * (3/6)^1 * (3/6) ^2

= 3 * 1/2 * 1/4

= 3/8

= 0.375

\((\frac{1}{2})^3*3 =\frac{3}{8} = 0.375\)

Answer: D

Given that a fair 6-sided die is rolled three times and We need to find What is the probability that the result of exactly one of the rolls will be an even number?

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 even number. This can happen by selecting 1 place out of 3 where even number will come.
=> 3C1 = 3 ways

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

=> Probability that exactly one of the rolls will be an even number = Place of that even number * Probability of getting an even number * Probability of getting an odd number * Probability of getting an odd number = 3 * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) = \(\frac{3}{8}\) = 0.375

So, Answer will be D
Hope it helps!

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


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