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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  [#permalink]

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New post 08 Jul 2019, 02:27
1
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A
B
C
D
E

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  25% (medium)

Question Stats:

66% (00:51) correct 34% (00:42) wrong based on 77 sessions

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Director
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Re: When two fair dice are rolled, what is the probability that at least  [#permalink]

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New post 08 Jul 2019, 02:32
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Bunuel wrote:
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


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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Re: When two fair dice are rolled, what is the probability that at least  [#permalink]

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New post 08 Jul 2019, 02:47
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Bunuel wrote:
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


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 [2C1 to select which of the two dice would be Even]

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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Re: When two fair dice are rolled, what is the probability that at least  [#permalink]

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New post 08 Jul 2019, 09:45
Bunuel wrote:
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


getting odd ; 3/6*3/6 ; 1/4
atleast 1 even ; 1-1/4; 3/4
IMO E
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When two fair dice are rolled, what is the probability that at least  [#permalink]

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New post 08 Aug 2019, 11:09
Prob of getting at least One even[P(A1E)] = 1- Prob of getting all odd [P(O)]

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
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When two fair dice are rolled, what is the probability that at least   [#permalink] 08 Aug 2019, 11:09
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