When two fair dice are rolled, what is the probability that at least

Question

When two fair dice are rolled, what is the probability that at least one of the numbers will be even?

(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4

CareerGeek · Accepted Answer

Probability of at least 1 even = 1 - Probability of no even(or Both odd)
= 1 - 3/6*3/6 
= 1 - 1/4
= 3/4

IMO Option E

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RJ7X0DefiningMyX · Answer

Couple of ways to solve this: Method 1: Case I - Exactly 1 Even (which means that the other one is Odd) = 2C1*3/6*3/6

Case II - Both Even = 3/6*3/6

Adding both the cases, we get 18/36 + 9/36 = 27/36 or 3/4

Method 2: Probability of No Even = Probability of Both Odd = 3/6*3/6 = 9/36

Probability of atleast 1 even = 1 - Probability of No Even = 1 - 9/36 = 27/36 or 3/4

Hence, the answer is (E) 3/4

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Archit3110 · Answer

getting odd ; 3/6*3/6 ; 1/4
atleast 1 even ; 1-1/4; 3/4
IMO E

fauji · Answer

Prob of getting at least One even  = 1- Prob of getting all odd

Total number of cases for 2 fair dice roll: 6*6 = 36
odd numbers: 1,3,5
So 3 cases each > 3*3 = 9 for both dice 
P(O) = 9/36 => 1/4

Now P(A1E) = 1 - 1/4 =>  3/4

Answer: Option  E

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=qAWzpEPPOWk

Given that Two dice are rolled and we need to find what is the probability that at least one of the numbers will be even?

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

Let's solve the problem using two methods:

Method 1:

Now there are 4 outcomes possible
(Odd, Odd), (Odd, Even), (Even Odd), (Even, Even) and there is an equal chance of each of them happening

=> P(At least one number is Even) = P((Odd, Even) or (Even Odd) or (Even, Even)) =  \frac{3}{4}

Method 2:

Out of the 36 comes lets eliminate all options in which both the outcomes are odd
Both can be odd in 3*3 (=9 ways), as in the first roll we can get any number out of 1, 3, and 5. And in the second case also we have these 3 choices.

=> P(At least one number is Even) =  \frac{36 - 9}{36}  =  \frac{27}{36}  =  \frac{3}{4}

So,  Answer will be E 
Hope it helps!

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

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

When two fair dice are rolled, what is the probability that at least

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When two fair dice are rolled, what is the probability that at least

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