A fair, six-sided die is rolled. What is the probability of obtaining a 3 or an odd number?
A. 1/6
B. 1/5
C. 1/4
D. 2/3
E. 1/2
GMAT Question of the Day : Probability
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E
E
E.
The prime numbers from 1-6 are 2, 3, and 5. The requirement of “3 or a prime number” includes 3, so your initial probability is 3/6. Reduce it and you get 1/2.
D
Thomas, it’s not prime numbers but odd numbers not that it would make any difference in the calculation in _this_ case
D
Probability of 3 is 1/6
Probability of 1,3,5 is 3/6
hence, 1/6 + 3/6 = 4/6 = 2/3
Pat – you can counting prob of getting 3 twice, it should be E:
Prob of getting 3 – 1/6
Prob of getting odd numbers (1 and 5 only, as prob of getting 3 is already calculated) – 2/6 = 1/3
So the final prob should be 1/6 + 2/6 = 1/2
Milind,
The probability of getting 3 has to be counted twice since getting a 3 or an odd numbers are independent events
Suppose question was like this:::
A fair, six-sided die is rolled. What is the probability of obtaining a 3 or an odd number or an even number ?
Then what would be the answer ?
What is the probability of obtaining a 3 or an odd number or an even number ?
3/6 + 3 /6 = 1.
Haa…If you roll a dice you have to get something…
i think its 1/6 + 1/2 = 2/3…. how do we know whether wat we said is corerct or not… pls get back..
That raises interesting possibilites Gmat Team!
Guess with that in view, the probability of the original question would be 1/2
Gangaraj, the answer will be revealed in the comments by 48 hours of the question being posted..
1/2
D
D it is
Prob of 3 = 1/6
Prob of odd number = 3/6 = 1/2
Hence required prob = 1/6 + 1/2 = 2/3
D (Guys where do we get the final correct answer. Please help GMAT team.)
Dear nakul_mukerjee,
At TakeGMAT.com we find answer through consensus as well as answer provided by TakeGMAT team.
d.
E
Answer is A
Probability of getting anything from a dice is 1/6
Trust me, I went to Las Vegas many many times !!! ( he he )
Just a quick question to TakeGMAT: Where do you find all these questions ? Are they “real” GMAT questions ?
Thanks for your hard work
Dear vietlonewolf,
Thanks a lot for your word of appreciation. All the questions are contributed by students like you as well as facultiese from http://www.achieverspoint.com
D
1
PRob of 3 or odd no. is 1/6 + 1/3
Prob of even no is 1/2
Final is 1/6+1/3+1/2 = 1
The ‘or’ indicates two mutually exclusive events
therefore
prob(A)=p(3)=1/6
prob(B)=P(oddnumber/1,3,5)=1/2
However Common part has to excluded
p(AXB/3)=1/6
i.e P(AorB)=p(A)+p(B)+P(A*B)
1/6+1/2-1/6=1/2
Ans is E.
(E)
The common part of two events should be excluded. Otherwise we will come to nonsense. Suppose the question asks “What is the probability of getting 1 or 2 or 3 or odd or even”. Correct questions, yes? Now if we just add the probs, we will get
1/6 + 1/6 + 1/6 + 3/6 + 3/6 = 9/6.
This is nonsense because prob can’t be > 1.
E
1 , 3 , 5 = 3/6 = 1/2
E
3/6 = 1/2
Dear Friends,
Ans is 2/3 (D)
Let me explain you one simple logic :
1)Whenever there is “OR” , we add the probabilities
2) Whenever there is “And”, we multiply the probabilities.
So here the questions asks us, what is the probability of getting 3 “or” an odd number (So here we will add)
Solution : Probability of Getting 3 is 1/6
Probability of getting odd number : 1/2
Now we need to add both the probabilities
1/6 + 1/2 = 2/3
Take gmat team, will you please confirm the same……..
With Regards
A.c.
hi guys the answer is 2/3 (D)
p(AUB)=P(A)+P(B)-P(A int b)
=1/6 + 1/2 = 1/3
wit regards,
Shree
No of ways we can get 3 is 1.
Total no of possible ways = 6.
Probability Of getting 3 is 1/6
No of ways we can get odd no is 3 [1 or 3 or 5] so 3 possible events.
Total no of possible ways is 6
Probability Of getting odd is 3/6
P(Getting 3 U Getting Odd) = P(A)+P(B) [note: here this is a single event.]
1/6 + 3/6 = 2/3
D: 1/6+3/6= 4/6 = 2/3
1/2
yeah, going by the logic of adding up
yeah, going by the logic of adding up probabilites of 2 events to calculate probability of either one happening leads us to a combined probability of 2/3…
even i calculated that and believed it to be right…
i thought, ‘they’ve not said probability of getting either a 3 OR ANOTHER odd number, right!!?!’…
turns out, one of those GMAT traps…
if we leave out working knowledge of probabilities as taught in school…
we realise that when a balanced 6 sided dice is rolled, whether 3 or any odd number, there are only three ways in total that either can show up — it could either be 1,3 or 5!!… three chances of six… hence 1/2 – da correct answer…
me too with E – 1/2
http://www.richland.edu/james/lecture/m170/ch05-rul.html
What we have here is Non-Mutually Exclusive Events, meaning the outcomes overlap, therefore the addition rule does not apply.
To quote from the website above: “In events which aren’t mutually exclusive, there is some overlap. When P(A) and P(B) are added, the probability of the intersection (and) is added twice. To compensate for that double addition, the intersection needs to be subtracted.”
As a result, we can see that
P(odd) = 1/2
P(3) = 1/6
P(intersection) = 1/6
P(odd) + P(3) – P(intersection) = 1/2
The ans is E : 1/2.
Eric confirms the exact logic behind.
Well Eric’s Link says everything .For OR condition to be valid Events should be mutually exclusive. So the answer is
P(3)=1/6
P(1,5)=2/6
P=1/6+1/3=1/2
E
Thats the answer!!!!
E
D…
When Does Take Gmat Answers, I have seen so many questions the does not answer.
Are the answers some where else.
Official Answer:: E
————————————————————-
Best Answer by @ERIC
What we have here is Non-Mutually Exclusive Events, meaning the outcomes overlap, therefore the addition rule does not apply.
To quote from the website above: “In events which aren’t mutually exclusive, there is some overlap. When P(A) and P(B) are added, the probability of the intersection (and) is added twice. To compensate for that double addition, the intersection needs to be subtracted.”
As a result, we can see that
P(odd) = 1/2
P(3) = 1/6
P(intersection) = 1/6
P(odd) + P(3) – P(intersection) = 1/2
E
E
e
its E, as probability = P(odd) + p(3)
But as P(3) is part of P(odd) so we can neglect it.
P(odd) = 1/2.(E).
E