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A greater than 50% chance that at least one was born in a leap year is the same as a less than 50% chance that none of them was born in a leap year.suchoudh wrote:What is the minimum number of randomly chosen people needed in order to have a better-than-50% chance that at least one of them was born in a leap year?
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
OA 3
Brent Hanneson wrote:A greater than 50% chance that at least one was born in a leap year is the same as a less than 50% chance that none of them was born in a leap year.suchoudh wrote:What is the minimum number of randomly chosen people needed in order to have a better-than-50% chance that at least one of them was born in a leap year?
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
OA 3
So, we can reword the question as, What is the minimum number of randomly chosen people needed in order to have a less than 50% chance that none of them was born in a leap year?"
Assuming that 3/4 is the probability that one is NOT born in a leap year, we can see that:
1 person: P(none born in a leap year) = 3/4 = 0.75 (nope, we want less than 0.5)
2 people: P(none born in a leap year) = 3/4 x 3/4 = 9/16 (nope, we want less than 0.5)
3 people: P(none born in a leap year) = 3/4 x 3/4 x 3/4 = 27/64 (this is less than 0.5)
The answer is 3
If you assume that the chance of being born on any particular day is that same as all other days, then 1 out of every 4 years is a leap year, so (ingoring the extra day which shifts the probabilities a tiny bit) there's a 1/4 chance of being born in a leap year and a 3/4 chance of being born in other years.sreak1089 wrote:Why do we need to assume that the probability that a person is NOT born in a leap year is 3/4?
Is it because 1/4 is the probability that a person is born in a leap year is 1/4?
Brent Hanneson wrote:A greater than 50% chance that at least one was born in a leap year is the same as a less than 50% chance that none of them was born in a leap year.suchoudh wrote:What is the minimum number of randomly chosen people needed in order to have a better-than-50% chance that at least one of them was born in a leap year?
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
OA 3
So, we can reword the question as, What is the minimum number of randomly chosen people needed in order to have a less than 50% chance that none of them was born in a leap year?"
Assuming that 3/4 is the probability that one is NOT born in a leap year, we can see that:
1 person: P(none born in a leap year) = 3/4 = 0.75 (nope, we want less than 0.5)
2 people: P(none born in a leap year) = 3/4 x 3/4 = 9/16 (nope, we want less than 0.5)
3 people: P(none born in a leap year) = 3/4 x 3/4 x 3/4 = 27/64 (this is less than 0.5)
The answer is 3
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