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# Two dice are thrown simultaneously. What is the probability of getting

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Intern
Joined: 24 Jul 2017
Posts: 12
Location: India
Schools: Copenhagen (A)
GMAT 1: 630 Q42 V34
GPA: 2.8
Two dice are thrown simultaneously. What is the probability of getting  [#permalink]

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27 Jan 2018, 07:39
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45% (medium)

Question Stats:

54% (01:16) correct 46% (01:29) wrong based on 52 sessions

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Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A) [1/2]

B) [3/4]

C) [3/8]

D) [5/16]

E) [5/6]
Math Expert
Joined: 02 Aug 2009
Posts: 7958
Two dice are thrown simultaneously. What is the probability of getting  [#permalink]

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27 Jan 2018, 07:55
sxsd wrote:
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A) [1/2]

B) [3/4]

C) [3/8]

D) [5/16]

E) [5/6]

Easier way is to find ways of ODD product..
each dice can show 1,3 or 5..
so ways of getting ODD product= $$3*3=9$$
Total ways to choose two numbers= $$6*6=36$$

ways of picking numbers such that product is even = 36-9=27

probability of picking even product = $$\frac{27}{36}=\frac{3}{4}$$
B

OR second way..

ways of getting even product..

1)first dice even number - 2,4 or 6- 3 ways
for these three even numbers, second dice can be any of 6 numbers - 6 ways
total ways = 3*6=18

2) first dice odd number = 1,3, or 5 -- 3 ways
for these three odd numbers, second dice has to throw even numbers so 2,4,6 - 3 ways
total 3*3 = 9 ways

total ways = 18+9=27
total ways of picking any two numbers = 6*6=36

prob = 27/36=3/4
B
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Joined: 26 Sep 2017
Posts: 95
Re: Two dice are thrown simultaneously. What is the probability of getting  [#permalink]

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28 Jan 2018, 12:19
1
1
sxsd wrote:
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A) [1/2]

B) [3/4]

C) [3/8]

D) [5/16]

E) [5/6]

Probability of both dice to be odd is = 3/6 * 3/6
= 1/4
So probability of even = 1- probability of odd
= 1-1/4
= 3/4

Sent from my BND-AL10 using GMAT Club Forum mobile app
CrackVerbal Quant Expert
Joined: 23 Apr 2019
Posts: 36
Re: Two dice are thrown simultaneously. What is the probability of getting  [#permalink]

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09 Oct 2019, 23:57
Hi,

While dealing with complex events in probability, the best way is to use the below equation to set up the question.

Probability (Complex event) = Probability (Individual Events) * arrangement

The complex event should always be represented by a set of alphabets, for example, if we need to find the probability of getting two heads and a tail when we toss a coin 3 times, then the probability can be represented as P(HHT).

P(HHT) = 1/2 * 1/2 * 1/2 * 3!/2! (3!/2! -----> arrangement of the word HHT)
P(HHT) = 3/8

Similarly here we need the probability of the product being even. There will be two cases here:

1. One number is even and one number odd, let us represent this as P(EO)

OR

2. Both numbers are even, let us represent this as P(EE)

P(EO) = 3/6 * 3/6 * 2! ----> 1/2

OR

P(EE) = 3/6 * 3/6 * 2!/2! -----> 1/4

1/2 + 1/4 = 3/4

Hope this helps!
Re: Two dice are thrown simultaneously. What is the probability of getting   [#permalink] 09 Oct 2019, 23:57
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