Question

what is the probability of getting 53 Tuesdays in (a) non leap year (2) leap year

Answer 1

Solution:

1) Non Leap year has 365 days

365days = 52 weeks + 1 day

Since, There are 52 weeks in a non leap year,

Therefore, There are minimum 52 Tuesday.

Now 1 additional day can be :

{ M , T , W , Th , F , Sa , S }
n(S) = 7

Probability of getting 53 Tuesday = Probability of getting Tuesday as extra day

So, P = 1/7

✌--------------------------------------✌

2) In Leap Year,

There are 366 days,

366 days = 52 weeks + 2days

These 2 days can be

{ MT , TW , WTh , ThF, FSa , SaS , SM}
n(S) = 7

Event , E: Getting Tuesday
n(E) = 2

Hence P(E) = n(E)/n(S) = 2/7

Answer 2

Solution:

.

1 year = 365 days A leap year has 366 days A year has 52 weeks. Hence there will be 52 Tuesdays for sure. 52 weeks = 52 x 7 = 364 days 366 – 364 =2 days In a leap year there will be 52 Tuesdays and 2 days will be left. These 2 days can be: Sunday, Monday Monday, Tuesday Tuesday, Wednesday Wednesday, Thursday Thursday, Friday Friday, Saturday Saturday, Sunday Of these total 7 outcomes, the favourable outcomes are 2. Hence the probability of getting 53 Tuesdays in a leap year = 2/7.