Question

13. (a) Find the probability of getting 53 Mondays in a non-leap year.
(b) Find the probability of getting 53 Fridays in a leap year.
(c) Find the probability of getting 52 Sundays in a leap year.​

Answer 1

Step-by-step explanation:

a) for non leap year there are 365 days in a year.

365 days =52 weeks and 1 day.

that remaining 1 day can be Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.

so total numer of outcomes =7

favorable outcome is Monday to have 53 Mondays in that year.

so total number of favorable outcome=1

Hence p(getting 53 Mondays in a non-leap year)=1/7

b) for leap year there are 366 days in a year.

366 days =52 weeks and 2 days.

that remaining 2 days can be (Sunday, Monday);(Monday ,Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday),(Friday,Saturday),(Saturday, Sunday)

so total numer of outcomes =7

favorable outcomes are (Thursday, Friday),(Friday,Saturday) to have 53 Fridays in that year.

so total number of favorable outcome=2

Hence p(getting 53 Fridays in a leap year)=2/7

c) for leap year there are 366 days in a year.

366 days =52 weeks and 2 days.

So it is a certain event to get 52 Sundays in a leap year.

Hence p(getting 52 Sundays in a leap year)=1