Question

find the probability that there are 53 mondays on a leap year....

Answer 1

Answer:

1 year = 365 days

A leap year has 366 days

A year has 52 weeks. Hence there will be 52 Mondays.

52 weeks = 52 x 7 = 364 days

366 – 364 =2 days

In a leap year there will be 52 Mondays 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 Mondays in a leap year P(E) = 2/7.

Answer 2

SOLUTION

TO DETERMINE

The probability of getting 53 Mondays in a leap year

EVALUATION

Leap year = 366 days

366 days = 52 weeks 2 days

Now 52 weeks contains 52 Sundays

2 days is one of the below

( Sunday, Monday), ( Monday, Tuesday), (Tuesday, Wednesday), ( Wednesday, Thursday), ( Thursday, Friday), ( Friday, Saturday ), (Saturday, Sunday)

So the total number of possible outcomes = 7

Let A be the event that of getting 53 Mondays ys in a leap year

So the total event points for the event A is ( Sunday, Monday), ( Monday, Tuesday)

So the total number of possible outcomes for the event A is 2

Hence the required probability

= P(A)

$\displaystyle \sf{ = \frac{Number \: of \: favourable \: cases \: to \: the \: event \: A }{Total \: number \: of \: possible \: outcomes }}$

$\displaystyle \sf{ = \frac{2}{7} }$

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