4d wrote:
Find the probability that a randomly selected year has 53 Sundays.
A) \(\frac{1}{7}\)
B) \(\frac{2}{7}\)
C) \(\frac{3}{7}\)
D) \(\frac{3}{28}\)
E) \(\frac{5}{28}\)
The question involves knowing leap year and number of days in a year..
So, let us talk of this question in two different cases..
(1) A normal year
It has 365 days which is 52 weeks and 1 day. So any of the 7 days from Sunday to Saturday that the year starts with will be 53 and rest 6 will be 52. Probability of Sunday will be as any of other seven so \(\frac{1}{7}\).
(2) A Leap year
It has 366 days which is 52 weeks and 2 days. So any 2 of the 7 days from Sunday to Saturday that the year starts with will be 53 and rest 5 will be 52. Probability of Sunday will be as any of other seven so \(2*\frac{1}{7}=\frac{2}{7}\). Multiplication by 2 is because we have 2 days that can be 53.
Now we have to check the probability of a normal year and a leap year.
Here, we will take a standard case that every 4th year is leap year and will not consider the 1000th year as non-leapso Probability of normal year is 3/4 and that of leap year is 1/4.
Answer \(\frac{3}{4}*\frac{1}{7}+\frac{1}{4}*\frac{2}{7}=\frac{5}{28}\)
E
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html
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