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30 Jan 2019, 22:23
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
28% (02:01) correct
72%
(01:28)
wrong
based on 69
sessions
History
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Not Attempted Yet
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) \(\frac{5}{28}\)
A) \(\frac{1}{7}\)
B) \(\frac{2}{7}\)
C) \(\frac{3}{7}\)
D) \(\frac{3}{28}\)
E) \(\frac{5}{28}\)
31 Jan 2019, 08:00
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4d
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-leap
so 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
Archit3110
31 Jan 2019, 09:25
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4d
Total days in year = 365 or say 52 weeks and 1 day
Total days in leap year = 366 days or say 52 weeks and 2 days
so P of sunday in non leap year = 1/7
and P of sunday in leap year = 2*1/7 ; reason why since we have a day extra in a leap year so chances are that sunday can be on that extra day
P of a leap year is 1/4 and non leap year is 3/4
so for sunday
1/4*2/7 + 3/4*1/7
2+3/28 ; 5/28
IMO E
