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The probability that Tom will win the Booker prize is 0.5, a
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07 May 2019, 02:02
07 May 2019, 02:02
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The probability that Tom will win the Booker prize is 0.5, and the probability that John will win the Booker prize is 0.4. There is only one Booker prize to win. What is the probability that at least one of them wins the prize?
(A) 0.2
(B) 0.4
(C) 0.7
(D) 0.8
(E) 0.9
(A) 0.2
(B) 0.4
(C) 0.7
(D) 0.8
(E) 0.9
Re: The probability that Tom will win the Booker prize is 0.5, a
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19 Oct 2019, 02:30
19 Oct 2019, 02:30
1
Hi Carcass, I found this same question on gmatclub at the link https://gmatclub.com/forum/topic238760.html
Since the question is ambiguous because it is not specified whether we should consider them winning the prize on the same year rather then in more than one competition, the answer was changed to E.
Since the question is ambiguous because it is not specified whether we should consider them winning the prize on the same year rather then in more than one competition, the answer was changed to E.
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Re: The probability that Tom will win the Booker prize is 0.5, a
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19 Oct 2019, 09:25
19 Oct 2019, 09:25
2
This question is a little ambiguous.
Are we saying that P(Tom wins the Booker prize) refers to the probability that Tom wins the prize AT SOME POINT in his life?
That is, he has more than 1 chance to win the prize? If that's the case, then it's possible that Tom AND John could both win the Booker Prize in different years.
If that's the case, then the correct answer is C.
Conversely, are we saying that P(Tom wins the Booker prize) refers to the probability that Tom wins the prize THIS YEAR?
If that's the case, then only one person can win the Booker prize this year, in which case the correct answer is E.
So, there are two possible ways to interpret this question.
-----------------------------------------------------------------------
Let's first examine the case in which P(Tom wins the Booker prize) refers to the probability that Tom wins the prize AT SOME POINT in his life.
Set-up:
If P(Tom wins) = 0.5, then P(Tom loses) = 0.5
Also, if P(John wins) = 0.4, then P(John loses) = 0.6
We want P(at least one of them wins the prize)
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(at least one of them wins the prize) = 1 - P(neither wins the prize)
P(neither wins the prize)
What needs to happen for neither person to win the Booker prize?
Well, Tom must lose AND John must lose.
So, (neither wins the prize) = P(Tom loses AND John loses)
= P(Tom loses) x P(John loses)
= 0.5 x 0.6
= 0.3
So, P(at least one of them wins the prize) = 1 - 0.3
=0.7
Answer:
-------------------------------------------------------
Case #2: P(Tom wins the Booker prize) refers to the probability that Tom wins the prize THIS YEAR?
In this case, only one person can win the Booker prize this year.
Here, P(at least one of them wins the prize) = P(Tom wins OR John wins)
Apply the OR probability formula: P(A or B) = P(A) + P(B) - P(A and B)
We get: P(Tom wins OR John wins) = P(Tom wins) + P(John wins) - P(Tom wins AND John wins)
= 0.5 + 0.4 - 0
= 0.9
Answer:
Are we saying that P(Tom wins the Booker prize) refers to the probability that Tom wins the prize AT SOME POINT in his life?
That is, he has more than 1 chance to win the prize? If that's the case, then it's possible that Tom AND John could both win the Booker Prize in different years.
If that's the case, then the correct answer is C.
Conversely, are we saying that P(Tom wins the Booker prize) refers to the probability that Tom wins the prize THIS YEAR?
If that's the case, then only one person can win the Booker prize this year, in which case the correct answer is E.
So, there are two possible ways to interpret this question.
-----------------------------------------------------------------------
Let's first examine the case in which P(Tom wins the Booker prize) refers to the probability that Tom wins the prize AT SOME POINT in his life.
Set-up:
If P(Tom wins) = 0.5, then P(Tom loses) = 0.5
Also, if P(John wins) = 0.4, then P(John loses) = 0.6
We want P(at least one of them wins the prize)
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(at least one of them wins the prize) = 1 - P(neither wins the prize)
P(neither wins the prize)
What needs to happen for neither person to win the Booker prize?
Well, Tom must lose AND John must lose.
So, (neither wins the prize) = P(Tom loses AND John loses)
= P(Tom loses) x P(John loses)
= 0.5 x 0.6
= 0.3
So, P(at least one of them wins the prize) = 1 - 0.3
=0.7
Answer:
Show: ::
C
-------------------------------------------------------
Case #2: P(Tom wins the Booker prize) refers to the probability that Tom wins the prize THIS YEAR?
In this case, only one person can win the Booker prize this year.
Here, P(at least one of them wins the prize) = P(Tom wins OR John wins)
Apply the OR probability formula: P(A or B) = P(A) + P(B) - P(A and B)
We get: P(Tom wins OR John wins) = P(Tom wins) + P(John wins) - P(Tom wins AND John wins)
= 0.5 + 0.4 - 0
= 0.9
Answer:
Show: ::
E
