Mathematics
Find the probability that the month of January may have 5 Mondays in
(i) a leap year
(ii) a non-leap year
Probability
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Answer
In January there are 31 days and in an ordinary year there are 365 days but in a leap year there are 366 days.
(i) In January of a leap year, there are 31 days i.e., 4 weeks and 3 days. Therefore we have to find the probability of having a Monday out of the remaining 3 days.
Now 3 days can be (Monday, Tuesday, Wednesday), (Tuesday, Wednesday, Thursday), (Wednesday, Thursday, Friday), (Thursday, Friday, Saturday), (Friday, Saturday, Sunday), (Saturday, Sunday, Monday), (Sunday, Monday, Tuesday).
In above 7 pairs, 3 times Monday occurs,
∴ Probability(having 5 Mondays) = .
Hence, the probability that the month of January may have 5 Mondays in a leap year is .
(ii) In January of an ordinary year, there are 31 days i.e. 4 weeks and 3 days. Out of remaining 3 days any one can be a monday,
Now 3 days can be (Monday, Tuesday, Wednesday), (Tuesday, Wednesday, Thursday), (Wednesday, Thursday, Friday), (Thursday, Friday, Saturday), (Friday, Saturday, Sunday), (Saturday, Sunday, Monday), (Sunday, Monday, Tuesday).
In above 7 pairs, 3 times Monday occurs,
∴ Probability (having 5 Mondays) = .
Hence, the probability that the month of January may have 5 Mondays in a non-leap year is .
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