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Math Expert V
Joined: 02 Sep 2009
Posts: 58464
Two six-sided dice with sides numbered 1 through 6 are rolled. If the  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 61% (01:46) correct 39% (01:29) wrong based on 67 sessions

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Two six-sided dice with sides numbered 1 through 6 are rolled. If the two resulting numbers are multiplied, what is the probability that their product will be even?

A. 1/12
B. 1/4
C. 1/2
D. 3/4
E. 11/12

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Intern  B
Joined: 18 Nov 2018
Posts: 27
Re: Two six-sided dice with sides numbered 1 through 6 are rolled. If the  [#permalink]

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1
D is the answer. Three scenarios:
P(dice 1 even) x P(dice 2 even) = 1/2 * 1/2= 1/4
P(dice 1 even) x P(dice 2 odd) = 1/2 * 1/2 = 1/4
P(dice 1 odd) x P(dice 2 even) = 1/2 * 1/2 = 1/4

P of the multiple to be even = 1/4 * 3 = 3/4
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Re: Two six-sided dice with sides numbered 1 through 6 are rolled. If the  [#permalink]

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Bunuel wrote:
Two six-sided dice with sides numbered 1 through 6 are rolled. If the two resulting numbers are multiplied, what is the probability that their product will be even?

A. 1/12
B. 1/4
C. 1/2
D. 3/4
E. 11/12

rolling of dice ending up even product
only possible under 3 cases
case1 : first dice even and other dice also even ; 3/6 * 3/6 = 1/4
case2 : first dice even and second dice odd ; 3/6 * 3/6 = 1/4
case 3: first dice odd and second dice even ; 3/6 * 3/6 = 1/4
so adding all cases 3/4
IMO D
Manager  P
Joined: 01 Feb 2017
Posts: 243
Re: Two six-sided dice with sides numbered 1 through 6 are rolled. If the  [#permalink]

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P(odd on both dices)= 1/2*1/2= 1/4

P(even)= 1-1/4 = 3/4

Ans D

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Manhattan Prep Instructor G
Joined: 04 Dec 2015
Posts: 832
GMAT 1: 790 Q51 V49 GRE 1: Q170 V170 Re: Two six-sided dice with sides numbered 1 through 6 are rolled. If the  [#permalink]

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Bunuel wrote:
Two six-sided dice with sides numbered 1 through 6 are rolled. If the two resulting numbers are multiplied, what is the probability that their product will be even?

A. 1/12
B. 1/4
C. 1/2
D. 3/4
E. 11/12

There are two tricks to this one.

The first is to realize what 'product is even' really means. It's really asking you for the probability that one or both numbers are even. If you're calculating products, you're solving this one incorrectly.

The second has to do with strategies for solving probability problems. To find a complicated probability ('one or both'), there are two basic approaches. One possibility is to divide up the probability into multiple smaller probabilities, then add or multiply those together as appropriate. In this case, you'd find three probabilities that don't overlap with each other:

- The probability that the first die is even and the second is odd;
- The probability that the first die is odd and the second is even;
- The probability that they're both even.

Then add those three up and you have your answer.

However, there's a quicker approach. If you can find the 'opposite' of your probability - the probability that it won't happen - you can just subtract that number from 1 to get your answer. In this problem, the only situation where the product won't be even is if both dice are odd. The probability of the first die being odd is 1/2, the probability of the second die being odd is 1/2, and so the probability that both are odd is 1/2 * 1/2 = 1/4. Then the answer to the question is 1-1/4 = 3/4.
_________________ Chelsey Cooley | Manhattan Prep | Seattle and Online

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Target Test Prep Representative D
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Joined: 14 Oct 2015
Posts: 8143
Location: United States (CA)
Re: Two six-sided dice with sides numbered 1 through 6 are rolled. If the  [#permalink]

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Bunuel wrote:
Two six-sided dice with sides numbered 1 through 6 are rolled. If the two resulting numbers are multiplied, what is the probability that their product will be even?

A. 1/12
B. 1/4
C. 1/2
D. 3/4
E. 11/12

We can use the equation:

P(even product) = 1 - P(odd product)

The possible pairs of numbers that yield an odd product are:

(1,1), (1,3), (1,5), (3,1). (3,3), (3,5), (5,1), (5,3), and (5,5)

The probability of each of these pairs is 1/36, so the total probability is 9/36 = 1/4.

Thus, P(even product) = 1 - 1/4 = 3/4.

Alternate Solution:

We can use the equation:

P(even product) = 1 - P(odd product)

Notice that the product of the outcome of the two dice is odd if and only if both of the numbers are odd. Since there is a 1/2 probability of obtaining an odd number for each die, the probability that both numbers are odd is 1/2 x 1/2 = 1/4. Thus, the probability of obtaining an even product is 1 - 1/4 = 3/4.

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