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Question
What is the probability that a leap year has 52 Mondays?
Options
\[\frac{2}{7}\]
\[\frac{4}{7}\]
\[\frac{5}{7}\]
\[\frac{6}{7}\]
Solution
A leap year
TO FIND: Probability that a leap year has 52 Mondays.
Total number of days in leap year is 366days
Hence number of weeks in a leap year is `366/7=52 "weeks and 2 day"`
In a leap year we have 52 complete weeks and 2 day which can be any pair of the day of the week i.e.
(Sunday, Monday)
(Monday, Tuesday)
(Tuesday, Wednesday)
(Wednesday, Thursday)
(Thursday, Friday)
(Friday, Saturday)
(Saturday, Sunday)
To make 52 Mondays the additional days should not include Monday
Hence total number of pairs of days is 7
Favorable day i.e. in which Mondays is not there is 5
`"We know that PROBABILITY" =" Number of favourable event"/"Total number of event"`
Hence probability that a leap year has 52 Mondays is equal to `5/7`
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