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]