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Minimum of how many people are needed to have the probability of more

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Minimum of how many people are needed to have the probability of more  [#permalink]

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New post 20 Aug 2018, 04:50
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GMAT CLUB TESTS' FRESH QUESTION:



Minimum of how many people are needed to have the probability of more than 1/2 that at lease one of them was born on either on Monday or on Tuesday?

A. 2
B. 3
C. 4
D. 5
E. 6

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Re: Minimum of how many people are needed to have the probability of more  [#permalink]

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New post 20 Aug 2018, 05:09
1
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:



Minimum of how many people are needed to have the probability of more than 1/2 that at lease one of them was born on either on Monday or on Tuesday?

A. 2
B. 3
C. 4
D. 5
E. 6



Say there are only 2 person..
Prob = 2/7+2/7-2/7*2/7=4/7-4/49=24/49<1/2
Ans will be 3 because with 2, we had answer almost close to 1/2
No calculations required therefore
B
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Re: Minimum of how many people are needed to have the probability of more  [#permalink]

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New post 20 Aug 2018, 05:13
chetan2u can you please explain a little bit more?

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Re: Minimum of how many people are needed to have the probability of more  [#permalink]

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New post 01 Oct 2018, 05:06
Need Expert to help with this one please!
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Re: Minimum of how many people are needed to have the probability of more  [#permalink]

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New post 01 Oct 2018, 06:38
2
Suppose there are 2 people A and B
Probability of one on monday/tuesday = 2c1 * 2/7 * 5/7
Prob of both on monday/tuesday = 2/7*2/7
Total = 20/4 + 4/49 = 24/49 < 1/2

Now increase the no of people to 3 : A, B and C
Prob of one on monday/tuesday = 3c1 * 2/7 * 5/7 * 5/7 = 150/343
Prob of two on monday/tuesday = 3c2 * 2/7 * 2/7 * 5/7 = 60/343
Prob of three on monday/tuesday = 2/7* 2/7 * 2/7 = 8/343

Total = 218/343 > 1/2
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Re: Minimum of how many people are needed to have the probability of more  [#permalink]

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New post 02 Oct 2018, 21:37
1
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:



Minimum of how many people are needed to have the probability of more than 1/2 that at lease one of them was born on either on Monday or on Tuesday?

A. 2
B. 3
C. 4
D. 5
E. 6

My approach was like this:
As, question stated that at least one of the people have to have birthday on either Monday or Tuesday, I need to figure out the probability of all of them having birthday on remaining 5 days of week (other than Monday and Tuesday), then simply asses the value whether it is less than 0.5. If it is less than 0.5 then we have our answer.
First option 2 people: probability of both of them having birthday of remaining 5 days out of 7 days : \(\frac{5}{7} * \frac{5}{7}\) =\(\frac{25}{49}\) > 0.5
2nd Option 3 people: probability of all 3 of them having birthday of remaining 5 days out of 7 days : \(\frac{5}{7}*\frac{5}{7}*\frac{5}{7} = \frac{125}{363}\)< 0.5 ---> so 3 people is our answer or option [B]
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Re: Minimum of how many people are needed to have the probability of more  [#permalink]

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New post 10 Oct 2018, 19:45
chetan2u wrote:
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:



Minimum of how many people are needed to have the probability of more than 1/2 that at lease one of them was born on either on Monday or on Tuesday?

A. 2
B. 3
C. 4
D. 5
E. 6



Say there are only 2 person..
Prob = 2/7+2/7-2/7*2/7=4/7-4/49=24/49<1/2
Ans will be 3 because with 2, we had answer almost close to 1/2
No calculations required therefore
B[/quote

Hi Experts,can you please explain Prob = 2/7+2/7-2/7*2/7 .
I am not able to understand this.
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Re: Minimum of how many people are needed to have the probability of more  [#permalink]

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New post 10 Oct 2018, 20:45
2
For "AT LEAST" probability question, it would be a good choice to use P(A) = 1 - P(not A)

Let's say
A - There is at least 1 person born on Monday or Tuesday
B - There is no one born on Monday or Tuesday
Clearly, P(A) = 1 - P(B)

The problem asks when P(A) > 1/2. Or in other words, when P(B) < 1/2.

If we have 1 person, P(B) = 5/7
If we have 2 people, P(B) = (5/7)^2 = 25/49
If we have 3 people, P(B) = (5/7)^3 = something that I am pretty sure that < 1/2

The correct answer is B.3
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Re: Minimum of how many people are needed to have the probability of more &nbs [#permalink] 10 Oct 2018, 20:45
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