Question

Find the probability that a leap year selected at random will contain 53 Tuesdays.

Answer 1

Hint- Check whether that additional two days of the leap year are Tuesday or not using the properties of probability, which tells how likely an event is going to occur or whether the proportion is true. The probability of an event lies between \[0\], and\[1\] where \[0\] denotes that event is not possible, whereas \[1\] denotes the certainty of events. Higher is the probability for the event higher will the chance for that event to occur.

Complete step by step solution:
Leap year has \[366\] days that occur every four years with the month of February having \[29\]days, which is an additional one day, whereas a non-leap year has February of 28 days. In general, a year have \[52\] weeks with one extra day, but a leap-year have\[52\]weeks with additional two day
A week have \[7\] days with all going to occur \[52\] times hence we get
\[52 \times 7 = 364\]Days
But a leap year has \[366\]days; hence we have \[\left( {366 - 364} \right) = 2\]days left.
These 2 days can be either (Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday).
Out of these 7 outcomes, 2 are favorable as there are 2 outcomes where Tuesday lies.
Hence, the probability of getting 53 Tuesdays\[ = \dfrac{2}{7}\]
Option A is correct.
Note: A year has 52 weeks with one additional day, which means each day of the week is going to occur 52 times with one extra day, which can be from Sunday to Saturday whereas a leap year has two extra days.